Systems and methods for high frequency impedance spectroscopy detection of daily changes of dielectric properties of the human body to measure body composition and hydration status

ABSTRACT

Systems and methods for high frequency impedance spectroscopy detection of daily changes of dielectric properties of the human body to measure body composition and hydration status. According to an aspect, a method at a computing device to determine a set of indirect dynamic human metabolism parameters includes using a sensor on an individual to acquire a set of electrical measurements. The method also includes combining a ratio technique with a canonical model form technique. The also includes performing a series of mathematical calculations on the acquired set of electrical measurements to determine the set of indirect dynamic human metabolism parameters for the individual based on the combined ratio technique and the canonical model form technique. The method further includes generating a trend regarding the set of indirect dynamic human metabolism parameters in response to performing the series of mathematical calculations on the acquired set of electrical measurements to determine the set of indirect dynamic human metabolism parameters for the individual.

CROSS REFERENCE

This application claims priority to U.S. patent application Ser. No.14/541,033, filed on Nov. 13, 2014, and titled AN APPARATUS AND METHODFOR THE ANALYSIS OF THE CHANGE OF BODY COMPOSITION AND HYDRATION STATUSAND FOR DYNAMIC INDIRECT INDIVIDUALIZED MEASUREMENT OF COMPONENTS OF THEHUMAN ENERGY METABOLISM, which claims priority to U.S. ProvisionalApplication Ser. No. 62/372,363, filed on Aug. 9, 2016, and titledAPPARATUS AND METHOD FOR ANALYSIS OF BODY COMPOSITION AND HYDRATIONSTATUS AND DYNAMIC INDIRECTED INDIVIDUALIZED MEASUREMENT OF COMPONENTSOF THE HUMAN ENERGY METABOLISM, the disclosures of which areincorporated herein by reference in their entireties.

TECHNICAL FIELD

Embodiments described herein relate to the analysis of body compositionand hydration status and dynamic indirect individualized measurement ofcomponents of the human energy metabolism. More particularly,embodiments described herein relate to the analysis of body compositionand hydration status and individualized mathematical modeling of thehuman energy metabolism relates generally to the measurement of theresistance and reactance of the human subject, to fitting mathematicalmodels to serial measurements of indirectly measured lean body mass andfat mass, and to performing minimum variance estimation and predictionof variable of the human energy metabolism.

BACKGROUND

Biomedical engineering tools and multiple patented inventions ofbioimpedance spectroscopy have been concerned with the problems ofmeasuring the resistance and reactance of the human body at a multitudeof frequencies in order to determine body composition and hydrationstatus. Advancements in mathematical modeling of the human energymetabolism have provided tools to describe the relationship betweenenergy balance, which is the difference of the energy intake and thetotal energy expenditure, and body composition changes. State spacemodeling coupled with the use of time variant minimum variance Kalmanfiltering or prediction has been successfully used in controlengineering for over 50 years to observe and control state variables ofcomplex dynamic systems. This technology holds great potential inmonitoring difficult to measure daily body composition changes alongwith other essential components of the human energy metabolism in orderto maximize capabilities of controlling them.

Bioimpedance spectroscopy has become a widely used technique in bodycomposition and hydration status analysis in recent decades. Themeasurement of impedance, which is measuring resistance and reactance atfrequencies from 1 to 1000 kHz, is purported to assist in thedetermination of extracellular and intracellular water mass. Accordingto the Cole model of body impedance as interpreted by Cornish¹, acurrent at low frequency flows through the extracellular water masswhile at higher frequencies it flows through both the extracellular andintracellular water mass, allowing for extracellular and total watermass measurements. The Cole model fitted to resistances and reactancesof the human subject at various frequencies can be extrapolated to theresistance values at zero and infinite frequencies. Using the resistancevalues at zero and an extrapolated infinite frequency, Moissl developedequations corrected with body mass index to calculate extracellular andintracellular water mass.² The problem with Moissl's equations was thatthey contained errors in the references, which accounted for the errorsin the body mass index corrected extracellular and intracellular watermass calculation's accuracy.³ ¹ Cornish, DOI:10.1088/0031-9155/38/3/001² Moissl, DOI: 10.1088/0967-3334/27/9/012³ Id.

The errors in bioimpedance measurements of extracellular andintracellular water have hampered their accuracy and reliability. Whenusing bioimpedance instruments, artefactual errors occur everywherealong the path of the flowing current around the entire electriccircuit, which consists of current sources, a human subject, measurementelectrodes, cable connections from subject to measuring instrument, andcalibration elements. One example of a disadvantage of the prior art isthat the errors due to offset voltage and voltage noise at nodaljunction points of the circuit elements cannot be determined, analyzed,and mitigated.⁴ ⁴ U.S. Pat. No. 5,280,429 (1994).

Moreover, at higher frequencies in bioimpedance spectroscopy, unexpectedphase shifts in the results occur due to human subject stray capacitanceand the instrument introduces distortions in the results due tononlinearity. Errors due to stray capacitance are unavoidable inpractice, uncontrollable to a large degree, and likely to be morepronounced where other devices are also attached to the subject, butthey are measurable. An example of a disadvantage of the prior art isthat the errors due to stray capacitances and other measuring errors areneither determined, nor analyzed, nor reduced.⁵ ⁵ Id.

Another problem with the current bioimpedance spectroscopy technology isthe variation in measurement results among machines due to the systemicerrors introduced by the techniques, the instrumentation used, and othererrors. Another example of the disadvantage of the prior art is that noeffort was made to measure quality and inform the user about the size ofthe detectable error during measurement and about the reliability of themeasurement results.⁶ ⁶ Id.

Another problem with bioimpedance measurements could be the placement ofthe preamplifier and the drivers of the shielded cables far away fromthe sensing electrodes. The disadvantage of such arrangements is thatthe magnitude of the interference from outside electromagnetic sourcesand the capacitive load from the shielded cables could cause suboptimalresults. The prior art uses Fast Fourier Transformation, substitutingsummation for integration and evaluating only two wavelengths.⁷ Thesesimplifications would be allowed if the analog to digital conversationwere accurate, which it is not. ⁷ Id.

With regard to measuring variable of human energy metabolism, decades ofresearch into the causes of the obesity epidemic and related scientificresearch for the cause of it led to the creation of mathematical modelsof obesity. These models were based on the first law of thermodynamicsand proffered that imbalance between energy intake and energyexpenditure lead to changes in energy storage, primarily in lipids. Theeffort to quantify changes of the lipid store led Hall to constructmathematical models describing body composition changes matched to groupaverages.⁸ However, everyone's metabolism has unique characteristics,and individualized modeling is needed. Further, there is a need forreal-time metabolic modeling and tracking. The Hall models⁹ work offline when all data are available for retrospective analysis.Differential equations with infinitesimal time resolution are used inthe Hall models, requiring significant software capacity to solve andknowledge of how the system changes during the 24 hour time period, whenneither is needed for real-time use and for measuring changes every 24hour period. Importantly, the Hall model equations do not succeed insatisfying the constraint of conservation of energy (i.e. the First Lawof Thermodynamics), at the end of each day, which is essential forindividualized real-time modeling. Further, Hall does not consider theconstraint that the model calculated body composition with its dailychange together with changes of hydration status have to add up to themeasured body weight and its daily change to allow for individualizedreal-time modeling. ⁸ Hall, DOI: 10.1152/ajpendo.00523; DOI:10.1109/MEMB.2009.935465; DOI: 10.1152/aj pendo. 00559.2009⁹ Hall, DOI:10.1152/ajpendo.00523; DOI: 10.1152/ajpendo.00559.2009

The imprecision of current methods for determining the variableassociated with body composition change, energy expenditure, and energyintake have precluded accurate quantification of the energy balance andthus precluded definitive statements regarding the cause of the obesityepidemic. The currently accepted method for tracking calorie intake inscientific studies of energy balance is self-reported calorie intakecounting. For example, the daily ingested calories broken down into thethree macronutrient groups are needed every day for the calculations inthe Hall models. However, self-reported calorie intake counting isfraught with systemic errors.¹⁰ ¹⁰ Hebert, DOI:10.1016/S1047-2797(01)00297-6

Model calculations of the macronutrient oxidation rate are an essentialcomponent of the modeling of the human energy metabolism. Hall createdmodels for the macronutrient oxidation rates.¹¹ However, Hall'sequations are ad-hoc and are inherently nonlinear and not suitable forinverse calculations when model input is sought from known model output.¹¹ Hall, DOI: 10.1152/ajpendo.00523; DOI: 10.1152/ajpendo.00559.2009

The problems of prediction and noise filtering also exist in the dynamicmodeling of the metabolism. The estimation or prediction of the statevariables of a dynamic system model poses the challenges of ensuringaccuracy and stability of estimations. Therefore, there is a need foraccurate and simplified tracking of body composition change, energyexpenditure, and especially energy intake exists.

With current clinical trial usage of the bioelectrical impedancemeasurement method, it has become quite apparent that there are severalshortcomings in clinical applications of the method. Some of theconcerns of clinical applications are summarized in Buchholtz¹² et al.Currently, the clinical applicability and the measurement accuracy arelimited to the group level only rather than providing accurate valuesspecific to an individual. The various bioelectrical impedance modelsand reference methods differ widely across studies. The results areconfusing for a clinician and they break down in disease states. ¹²Buchholtz et al, DOI: 10.1177/0115426504019005433

There is no consensus on which commercially available biomedicalimpedance instruments are the best and which electrophysiological modelsbest describe the human body in vivo. Some of the shortcomings of thecurrent instrumentation include but are not limited to: lack of qualitymeasurements of the electrode placement and electrical properties ofelectrodes during measurements, lack of error calculations, noelimination of flawed data, no error calculations for the model fitting,no overall quality measurements regarding results, and no use ofstatistical improvement of errors when serial measurements are takenfrom an individual.

Currently, there is no systematic effort to register important butinfluencing factors on the measurements such as environmental factorsincluding location and room temperature to measure and compensate forlocal environmental electromagnetic influences. There is no systematiceffort to register physiological factors such as accurate body weight,time of the measurement, duration of measurement, skin temperature,recent exercise status, fluid and food consumption diary, timing of lastbladder emptying, and bowel movement among others.

The simplistic use of the Cole model is inadequate to capture importantchanges regarding conductivity and permittivity¹³ which occur duringacute changes of hydration. The impedance models currently in use failto predict changes of extracellular water and total body water duringshort term 2-3% dehydration and rehydration.¹⁴ The Cole model is notindividualizable to suit current demand. ¹³ Gerritsen et al,DOI:10.1088/1742-6596/434/1/012005¹⁴ Asselin et al, DOI:10.1016/S0969-8043(97)00179-6

The problems of measuring hydration status changes with currentbioimpedance methods carry over to the problem of measuring bodycomposition changes. The current methods of measuring body compositionchanges with the bioimpedance spectroscopy method rely primarily on thedetermination of extracellular as well intracellular water masses.

Current bioimpedance spectroscopy methods revealed significantsystematic errors in the difference between fluid volumes and thereference in the extremes of body mass index.¹⁵ These significantsystematic errors are due to large variations of the calculatedresistances at zero and infinite frequencies, suggestive of theinadequacy of the applied Hanai mixture theory applied together with theCole model to describe human immittance. ¹⁵ Moissl, DOI:10.1088/0967-3334/27/9/012

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter.

Disclosed herein are systems and methods for high frequency impedancespectroscopy detection of daily changes of dielectric properties of thehuman body to measure body composition and hydration status. Accordingto an aspect, a method at a computing device to determine a set ofindirect dynamic human metabolism parameters includes using a sensor onan individual to acquire a set of electrical measurements. The methodalso includes combining a ratio technique with a canonical model formtechnique. The also includes performing a series of mathematicalcalculations on the acquired set of electrical measurements to determinethe set of indirect dynamic human metabolism parameters for theindividual based on the combined ratio technique and the canonical modelform technique. The method further includes generating a trend regardingthe set of indirect dynamic human metabolism parameters in response toperforming the series of mathematical calculations on the acquired setof electrical measurements to determine the set of indirect dynamichuman metabolism parameters for the individual.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing summary, as well as the following detailed description ofvarious embodiments, is better understood when read in conjunction withthe drawings provided herein. For the purposes of illustration, there isshown in the drawings exemplary embodiments; however, the presentlydisclosed subject matter is not limited to the specific methods andinstrumentalities disclosed.

FIGS. 1A and 1B depict flowcharts illustrating how the measurements of adevice for body composition and hydration status analysis flow into amethod for dynamic indirect individualized measurement of components ofthe human energy metabolism.

FIG. 2 is an interface electrical connection between a human subject andmeasuring points.

FIG. 3 is an input logic circuit connecting measuring points.

FIG. 4 is the measuring circuit of the first embodiment configured todetermine the impedance of a human subject at various frequencies.

FIGS. 5A, 5B, 5C, 5D, 5E, 5F, 5G, 5H, 5I, 5J, 5K, 5L, 5M, 5N, 5O, 5P,5Q, 5R, 5S, 5T, 5U and 5V are flowcharts illustrating the analysis ofchange of body composition and hydration status and the dynamic indirectindividualized measurement of components of the human energy metabolism,including an R-ratio method using a Canonical Model Form of the HumanEnergy Metabolism method and estimating the daily energy density of thelean body mass change, the daily energy density of the fat mass change,and the daily ratio of lean body mass change velocity and fat masschange velocity or equivalently R-ratio.

FIG. 6 shows an example arrangement of two voltage sources, twoexcitation electrodes and one sensing electrode for each foot.Represented are the four reference resistances and the five voltagemeasuring points and the model circuit elements of the complex humanimpedances of both feet. Depicted are the measured segment of the humanbody including stray capacitances of the human body, the resistance atan estimated zero frequency, resistance of an extrapolated infinitefrequency, and the membrane capacitance.

FIGS. 7A, 7B, 7C, 7D, 7E, 7F, 7G, 7H, and 7I show the flowcharts of theoperation with three parts wherein the first part contains three stages,the second part two stages, and the third part three stages ofoperation.

DETAILED DESCRIPTION

The presently disclosed subject matter is described with specificity tomeet statutory requirements. However, the description itself is notintended to limit the scope of this patent. Rather, the inventor hascontemplated that the claimed subject matter might also be embodied inother ways, to include different steps or elements similar to the onesdescribed in this document, in conjunction with other present or futuretechnologies. Moreover, although the term “step” may be used herein toconnote different aspects of methods employed, the term should not beinterpreted as implying any particular order among or between varioussteps herein disclosed unless and except when the order of individualsteps is explicitly described.

Articles “a” and “an” are used herein to refer to one or to more thanone (i.e. at least one) of the grammatical object of the article. By wayof example, “an element” means at least one element and can include morethan one element.

In this disclosure, “comprises,” “comprising,” “containing” and “having”and the like can have the meaning ascribed to them in U.S. Patent lawand can mean “includes,” “including,” and the like; “consistingessentially of” or “consists essentially” likewise has the meaningascribed in U.S. Patent law and the term is open-ended, allowing for thepresence of more than that which is recited so long as basic or novelcharacteristics of that which is recited is not changed by the presenceof more than that which is recited, but excludes prior art embodiments.

Ranges provided herein are understood to be shorthand for all of thevalues within the range. For example, a range of 1 to 50 is understoodto include any number, combination of numbers, or sub-range from thegroup consisting 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, or 50.

Unless specifically stated or obvious from context, as used herein, theterm “about” is understood as within a range of normal tolerance in theart, for example within 2 standard deviations of the mean. About can beunderstood as within 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, 0,5%,0.1%, 0.05%, or 0.01% of the stated value. Unless otherwise dear fromcontext, all numerical values provided herein are modified by the termabout.

Unless otherwise defined, all technical terms used herein have the samemeaning as commonly understood by one of ordinary skill in the art towhich this disclosure belongs.

According to one or more aspects, several advantages of the analysis ofchange of body composition and hydration status over the prior artinclude, but are not limited to:

-   -   1. Measuring and correcting for stray capacitance.    -   2. Positioning the preamplifiers and the shield drivers close to        the sensing electrodes.    -   3. Analyzing and removing errors and noise in the measuring        circuit by using an input logic circuit.    -   4. Possessing a current source designed for high output        resistance and low output reactance.    -   5. Using a sine wave fitting algorithm.    -   6. Using a non-linear curve fitting algorithm.    -   7. Creating individualized references for the measurement of        body composition and hydration status change.

Regarding measuring and correcting for stray capacitance, one aspectmeasures all capacitances including stray capacitances. One aspectmeasures the voltage at 6 measuring points along the current path. Oneaspect applies Kirchhoff's first and second rule and Ohm's rule. Allmeasurements have amplitude, offset, and phase value and one aspectcompares them to the zero phase value measured at reference resistances.The advantage of measuring voltage at nodal junctions and applyingKirchhoff's rules and Ohm's rule is that it is possible to calculate thestray capacitance and measure its influence on the results.

Regarding positioning the preamplifiers and the shield drivers close tothe sensing electrodes, the advantage of one aspect is positioning thepreamplifiers and the shield drivers close to the sensing electrodes sothat the input noise will be kept low and no additional noise orcapacitive load will be added.

Regarding analyzing and removing errors and noise in the measuringcircuit by using an input logic circuit, one aspect use switches toisolate or short circuit or leave intact parts of the measuring circuitwithout or with excitation at various frequencies. This allows fordetermining errors due to offset voltage and voltage noise due tovarious sources. The offset voltage is eliminated by subtracting themeasured values at nodal junctions from the measured signal via asoftware algorithm. Hardware and/or software filtering remove voltagenoise. One advantage of using an input logic circuit is that theapparatus will sense the offset voltage and voltage noise in theenvironment of operation and this allows for reduction of offset voltageand voltage noise.

Regarding a current source designed for high output resistance and lowoutput reactance, one aspect uses two mirrored Howland current sourceswhich are fine tuned for their passive components to achieve high outputresistance and low output reactance.¹⁶ This mirrored arrangement has theadvantage that the output reactance is cut in half. One aspect uses tworeference resistances for each current source. Using two referenceresistances for each current source has one advantage such that thecurrent generated or sunk into the circuit will be known for eachcurrent source, allowing for precise network analysis. Using twomirrored Howland current sources has another advantage of creating avirtual floating earth potential, avoiding electric charge build up onthe sensing electrodes. ¹⁶ Bertemes-Filho, DOI:10.4236/cs.2013.47059

Regarding use of a sine wave fitting algorithm, sine wave fitting hasthe advantage of providing a priori knowledge of the exact value of theapplied frequency of excitation, reducing the number of unknownvariables. In statistical terms, sine fitting provides the minimumvariance linear estimation for amplitude, phase, and offset. Sinefitting compensates better for the errors of the analog digitalconversion than the Fast Fourier Transformation, which remains sensitiveto such errors.¹⁷ Using a sine wave fitting algorithm over 6 to 16wavelengths minimizes sampling error of the analog to digital converter.The sine fitting algorithm also gives a residual value, which one aspectuses to measure quality. One advantage of using the sine fittingalgorithm is better overall noise reduction, allowing for elimination ofoffset voltage, minimization of voltage noise, and the ability tomeasure quality. ¹⁷ Bertocco, DOI:10.1109/19.571881

Regarding using a non-linear curve fitting algorithm, a Cole model withunknown resistance at zero and an extrapolated infinite frequency andunknown membrane capacitance may be fitted to the resistance andreactance values at each examined frequency. The residual value,calculated as the difference between the measured and the modelpredicted value, may be used to measure the quality of each individualmeasurement at each frequency. The sum of squared residual values thusmeasures the overall performance of the first embodiment of one aspectof the apparatus. The advantage of measuring performance using the sumof squared residual values is that the user obtains quantifiedinformation of performance and of reliability of the function of theapparatus.

Regarding creating individualized references for the measurement of bodycomposition and hydration status change, one aspect overcomes theproblem that the equations corrected with body mass index contain errorsin the references by establishing individual references forextracellular and intracellular water mass. One advantage of creatingindividualized references is that all of my measurements areindividualized, referenced to individual reference values.

According to one or more aspects, several advantages of dynamic indirectindividualized measurement of components of the human energy metabolismover the prior art include, but are not limited to:

-   -   1. Having an individualized self-correction and self-adaptive        modeling.    -   2. Having a real-time calculation with recursive formulas and        daily updates.    -   3. Applying linear invertible models.    -   4. Using difference equations.    -   5. Having a state space method.    -   6. Calculating macronutrient oxidation rates.    -   7. Calculating daily utilized macronutrient intake values from        ingested macronutrient calorie intake.    -   8. Using the law of conservation of energy.    -   9. Estimating the daily utilized macronutrient intake values        from indirectly measured body composition changes.    -   10. Estimating the daily changes of the body composition and        stochastic identification of the unidentified energy losses or        gains, correction factor of the de novo lipogenesis, and        correction factor for gluconeogenesis.    -   11. Deriving the Canonical Model Form of the Human Energy        Metabolism.    -   12. Deriving a daily energy density of the lean body mass change        and the daily energy density of the fat mass change.    -   13. Estimating the daily ratio of lean body mass change velocity        and fat mass change velocity or equivalently R-ratio.

Regarding individualized self-correcting and self-adaptive modeling, oneaspect is achieved through serial measurements of body compositionchanges and adjustment of the model parameters in a way that the modelcalculations approach the indirectly measured body composition changesor a target trajectory. Individualized self-correcting and self-adaptivemodeling has one advantage of reflecting the state of the individualenergy metabolism better than previous models, which were adjusted togrouped or averaged data points of a population.

Regarding real-time calculations with recursive formulas and dailyupdates, one aspect uses models that use recursive formulas which areupdated daily with new data, eliminating the need to know all previousdata points except for the last day's data during update and allowingfor real-time calculations of changes of body composition as they occur.The recursive method preserves the information gained from the lastday's data without the need to store the information in the memory forcalculations. One advantage of an algorithm using a recursive structureis that it is easy to use on portable computer devices and allows formaking indirect measurements in freely moving human subjects.

Regarding applying linear invertible models, the nonlinear equationsused in the Hall model are very difficult or sometimes impossible toinvert in order to calculate an unidentified input, the utilized energyintake from a known output, the body composition change and energyexpenditure. Also, the thermic effect of feeding is calculatedimplicitly in the Hall models, making inverse calculations to determineutilized energy intake rather difficult. It has also been found thatadaptive thermogenesis, as modeled by Hall with an ad-hoc formula,requires unnecessary assumptions and model parameter determinations whenindirect measurement of the body composition can provide thisinformation.

The model equations of one aspect are linear and structured to supportinverse calculations for unknown input variables, allowing forcalculating the unknown macronutrient energy intake. One advantage of alinear invertible model is that by measuring the body composition changeand using an inverse calculation, one aspect determines the difficult tomeasure utilized macronutrient intake which was necessary to produce themeasured body composition change in a freely moving human subject.

Regarding using difference equations, rather than using differentialequations, which require continuous measurements and elaborateintegration methods to solve, one aspect uses difference equations with24 hour time resolution requiring model calculations only every 24hours. The calculations require only matrix operations, eliminating theneed for the knowledge of the exact course of changes during the 24 hourperiod. One advantage of using difference equations is that the explicitknowledge of how the metabolism arrived at the measured new state ofbody composition after a 24 hour time span is not required.

Regarding using the state space method, the state space method allowsfor interfacing error containing measurements through the use of ameasurement model to a process model describing the metabolic process.The state space method provides a convenient framework for theimplementation of the time variant minimum variance Kalman estimation orprediction method.

Regarding calculating macronutrient oxidation rates, it has been foundthat macronutrient oxidation of carbohydrate, fat, and protein can bemodeled for inverse calculation purposes using the principles ofindirect calorimtry.¹⁸ One aspect uses the formulas introduced byLivesey, G. and Elia, M. to calculate macronutrient oxidation.¹⁹ Oneadvantage of using these formulas is that they can be directly appliedto the self-adaptive individualized metabolic model of the human energymetabolism of one aspect because they are linear and suitable forinverse calculations when model input is sought from known model output.¹⁸ Indirect calorimetry: methodological and interpretative problems,American Journal of Physiology—Endocrinology and Metabolism. March 1990;258(3):E399-E412¹⁹ Livesey, G. and M. Elia. Estimation of energyexpenditure, net carbohydrate utilization, and net fat oxidation andsynthesis by indirect calorimetry: evaluation of errors with specialreference to the detailed composition of fuels. American Journal ofClinical Nutrition. April 1988; 47(4):608-628

Regarding calculating utilized macronutrient intake values from ingestedmacronutrient calorie intake, the input to the equations of one aspectis the daily utilized macronutrient energy intake without thermic effectof feeding and the energy losses due to incomplete absorption. Oneaspect calculates the thermic effect of feeding and the energy lossesdue to incomplete absorption from tabled values.^(°)The thermic effectof feeding and the energy losses due to incomplete absorption aresubtracted from the ingested calories to obtain the daily utilizedcarbohydrate, fat, and protein intake. Calculating the daily utilizedmacronutrient values has one advantage that inverse calculations of theutilized energy intake become independent from the individual thermiceffect of feeding or food absorption variables. ²⁰ Food and NutritionBoard, Institute of Medicine. Dietary Reference Intakes for Energy,Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and AminoAcids (Macronutrients): A Report of the Panel on Macronutrients,Subcommittees on Upper Reference Levels of Nutrients and Interpretationand Uses of Dietary Reference Intakes, and the Standing Committee On theScientific Evaluation of Dietary Reference Intakes.http://www.nap.edu/books/0309085373/html/

Regarding using the law of conservation of energy, the energy equationsof one aspect take into account all major known processes of the humanenergy metabolism and are built to satisfy the law of conservation ofenergy at the end of a 24 hour period. One aspect accommodates the sofar unknown energy forms in the energy balance equation by using acorrection factor for unknown energy losses or gains. Including acorrection factor for unknown energy losses or gains has one advantageof balancing the energy equations of one aspect so that they satisfy thelaw of conservation of energy. The correction factor for unknown energylosses or gains also serves as a measure of performance of the model ofone aspect, since the major components of the energy equation areincluded in the model of one aspect and the expectation is that theunknown energy forms remain small.

Regarding estimating the daily utilized macronutrient intake values fromindirectly measured body composition changes, one aspect uses the timevariant Kalman prediction method with innovations representation forprediction and estimation of the unknown utilized macronutrientintake.²¹ For estimating the error of estimation, one aspect uses areference or nominal trajectory method.²² The reference or nominaltrajectory method has one advantage of enhancing the accuracy andstability of estimations. One advantage of utilizing the Kalmanprediction, innovations representation, and the reference or nominaltrajectory method is that is possible to estimate the daily utilizedmacronutrient intake in a freely moving human subject and requires onlydaily measurement of the physical energy expenditure and determinationof the body composition change along with an infrequently usedcalibration procedure. ²¹ Ljung, L. and T. Soderstrom. Theory andPractice of Recursive Identification. 1983; MIT Press, Cambridge,Massachusetts, pp. 125²² Jazwinski, A. W. Stochastic Processes andFiltering Theory. 1970; Academic Press, Inc. New York, pp. 376

Regarding estimating the daily changes of the body composition andstochastic identification of the unidentified energy losses or gains,correction factor of the de novo lipogenesis, and correction factor forgluconeogenesis, one aspect uses the time variant Kalman filteringmethod with innovations representation for estimation of the daily bodycomposition change. One aspect calculates the unknown energy losses orgains, the correction factor for de novo lipogenesis, and the correctionfactor for gluconeogenesis from amino acids with a stochasticidentification method.²³ One aspect uses a reference or nominaltrajectory method for estimating the daily body composition changes.²⁴The method of one aspect has the advantage of enhancing accuracy andstability of estimations of daily body composition changes and allowingfor dynamic indirect individualized measurement of components of thehuman energy metabolism in a freely moving human subject requiring onlydaily measurement of the physical energy expenditure and thedetermination of the body composition change along with an infrequentlyused calibration procedure for body composition and hydration statuschange. ²³ Walter, E. and L. Pronzato. Identification of ParametricModels from Experimental Data. 1997; Springer Verlag Berlin, Paris, NewYork. pp. 114²⁴ Jazwinski, A. W. Stochastic Processes and FilteringTheory. 1970; Academic Press, Inc. New York, pp. 376

Regarding deriving the Canonical Model Form of the Human EnergyMetabolism, in computer science when representing mathematical objectsin a computer, there are usually many different ways to represent thesame object. In this context, a canonical form is a representation suchthat every object has a unique representation. Thus, the equality of twoobjects can easily be tested by testing the equality of their canonicalforms. Here, one aspect uses a canonical representation of the humanenergy metabolism. One advantage of using such a representation is thatthe calculated metabolic parameters allow for intra- as well asinter-individual comparisons of the indirectly measured metabolicparameters. This allows quantitative characterization of the metabolismand enhances understanding of individual variations and predicts theeffect of dietary and exercise interventions.

Regarding daily energy density of the lean body mass change and thedaily energy density of the fat mass change, central to the developmentof the canonical representation of the energy metabolism is to quantifythe relationship between total energy balance and daily lean body massand fat mass change. One aspect uses a method to quantify this energyrelationship by estimating the daily energy density of the lean bodymass change and the daily energy density of the fat mass change. Oneadvantage is that long term trends or trajectories of the lean body massand fat mass changes can be estimated to predict future changesquantitatively.

Regarding estimating the daily ratio of lean body mass change velocityand fat mass change velocity or equivalently R-ratio, the association ofobesity with type 2 diabetes has been recognized to be in large part dueto insulin resistance and consequential hyperinsulinemia. Insulinresistance and ensuing high average level of insulin promotes amongother processes of lipogenesis and diminishes triglyceride breakdown byinhibiting lipolysis. Further, the mobilization of fat from the fatstores between meals is reduced, resulting in a surplus of fatty acid atthe cellular level, which creates a state described as lipotoxicity.²⁵Lipotoxicity is linked to decreased fat oxidation leading to impairedcapability of losing weight intentionally. One aspect uses a surrogatemeasure for insulin resistance called “R-ratio”. This ratio establishesa quantitative relationship between daily lean body mass change velocityand fat mass change velocity. Practical, stable methods are used toestimate this relationship. One advantage is that the R-ratio showsstrong correlation with other surrogate markers of insulin resistancesuch as the HOMA-IR (homeostasis assessment model of insulin resistance)and appears to be promising for non-invasive tracking of the insulinresistance change. The calculated correlation coefficient between theR-ratio and HOMA-IR is −0.8383 with P value of 0.0093 and was found byusing data from the Dietary Weight Loss and Exercise Effects on InsulinResistance in Postmenopausal Women.²⁶ ²⁵ Lelliott, DOI:10.1038/sj.ijo.0802854²⁶ Mason, DOI: 10.1016/j.amepre.2011.06.042

FIGS. 1A and 1B illustrate how the measurements of a first embodimentfor body composition and hydration status analysis 109 flows into amethod 130 for dynamic indirect individualized measurement of componentsof the human energy metabolism, and this method 130 is illustrated indetail in the flowchart in FIG. 5A to 5V.

A human subject 105 undergoes a body composition change of his or herglycogen store, fat store, and protein store on an examined day k. Atotal energy expenditure 101 is produced on day k and leaves the humansubject 105 on day k. Energies enter the human subject 105 in the formof the ingested carbohydrate intake 102, fat intake 103, and proteinintake 104 on day k. A device for body composition and hydration statusanalysis 109 measures resistance directly at multiple frequencies andextrapolated indirectly to a zero frequency and an extrapolated infinitefrequency on day k 106. The same device for body composition andhydration status analysis 109 measures the extracellular water mass onday k 126, the intracellular water mass on day k 127, and the change oflean body mass and fat mass on day k 107. The same device 109 canoptionally measure acute change of extracellular water mass andintracellular water mass 108. A measurement of physical activity energyexpenditure 110 is required on day k. Optional measurements of ingestedenergy in the form of carbohydrate 111, fat 112, and protein 113 aretaken on day j for calibration purposes. An optional measurement ofresting metabolic rate 114 is taken on day j for calibration purposes.An optional measurement of nitrogen excretion 115 is taken on day j forcalibration purposes and to indirectly measure the dailygluconeogenesis. An optional measurement of the rate of endogenouslipolysis 116 is taken on day j for calibration purposes and toindirectly measure the daily lipolysis. The method for dynamic indirectindividualized measurement of components of the human energy metabolism130 comprises a Self-Correcting Model of the Utilized Energy Intake 131,a Self-Adaptive Model of the Human Energy Metabolism 132, and acalculation of the components of the human energy metabolism 133. TheSelf-Correcting Model of the Utilized Energy Intake 131 estimates theutilized energy intake, defined as the daily utilized energy ofcarbohydrate, fat, and protein caloric intake 119. The Self-AdaptiveModel of the Human Energy Metabolism 132 estimates the daily change ofbody composition, defined as the change of glycogen store, fat store,and protein store 118. The calculation of the components of the humanenergy metabolism 133 provides the macronutrient oxidation rate results,defined as the daily rate of carbohydrate oxidation, fat oxidation, andprotein oxidation 120; daily resting metabolic rate 121; daily unknownforms of energy losses or gains 122; daily rate of endogenous lipolysis123; daily nitrogen excretion 124; and daily gluconeogenesis fromprotein 125.

FIG. 2 illustrates an interface electrical connection between the humansubject 105 and measuring points 1, 208, measuring point 3, 211,measuring point 4, 213, and measuring point 5, 215. The same figure alsoshows the lumped circuit diagram equivalent of the human subject 105connected to nodal junctions 216 and 217. The lumped circuit diagram ismade up of the resistance at an estimated zero frequency 205 connectedparallel to the serially connected membrane capacitance 207 andresistance at an extrapolated infinite frequency 206. Nodal junction 216is also connected to earth potential 202 through stray capacitance 1,204. Nodal junction 216 is also connected to measuring point 1, 208through excitation electrode resistance 1, 209, and to measuring point3, 211, through Sensory electrode resistance 1, 210. Nodal junction 217is also connected to earth potential 202 through stray capacitance 2,203. Nodal junction 217 is also connected to measuring point 5, 215through excitation electrode resistance 2, 214 and to measuring point 4,213 through sensory electrode resistance 2, 212. I model the humanimpedance with a Cole circuit model consisting of a resistance at anestimated zero frequency 205 connected parallel to the seriallyconnected membrane capacitance 207 and resistance at an extrapolatedinfinite frequency 206. This Cole circuit model provides the impedanceof the human subject 105.

FIG. 3 illustrates an input logic circuit connecting measuring point 1,208, measuring point 3, 211, measuring point 4, 213, and measuring point5, 215, which are in close proximity to the human subject 328, withmeasuring point 1, 208, measuring point 3, 211, measuring point 4, 213,measuring point 5, 215, and measuring point 6, 325, inside of a devicefor body composition and hydration status analysis 327. Measuring point1, 208, in close proximity to the human subject 328, is connected tomeasuring point 1, 208, inside of the device for body composition andhydration status analysis 327, through on and off switch 14, 310.Measuring point 1, 208, in close proximity to the human subject 328, isalso connected to measuring point 6, 325, inside of the device for bodycomposition and hydration status analysis 327, through referenceresistance 1, 324. Measuring point 3, 211, in close proximity to thehuman subject 328, is directly connected to measuring point 3, 211,inside of a device for body composition and hydration status analysis327. Measuring point 4, 213, in close proximity to the human subject328, is directly connected to measuring point 4, 213, inside of a devicefor body composition and hydration status analysis 327. Measuring point5, 215, in close proximity to the human subject 328, is connected tomeasuring point 5, 215, inside of the device for body composition andhydration status analysis 327, through on and off switch 13, 322.Measuring point 5, 215, in close proximity to the human subject 328, isconnected to measuring point 2, 320, inside of the device for bodycomposition and hydration status analysis 327, through referenceresistance 2, 321. Measuring point 5, 215, in close proximity to thehuman subject 328, is connected to measuring point 0, 319, inside of thedevice for body composition and hydration status analysis 327, throughon and off switch 7, 312.

Measuring points 1, 3, 4, and 5, 208, 211, 213, and 215, respectively,in close proximity to the human subject 328, are connected through onand off switches 1-6, 306, 307, 305, 309, 308, and 311, respectively.Measuring point 1, 208, is connected to measuring point 3, 211, throughon and off switch 2, 307. Measuring point 1, 208, is connected tomeasuring point 5, 215, through on and off switch 4, 309. Measuringpoint 1, 208, is connected to measuring point 4, 213, through on and offswitch 5, 308. Measuring point 3, 211, is connected to measuring point4, 213, through on and off switch 1, 306. Measuring point 3, 211, isconnected to measuring point 5, 215, through on and off switch 6, 311.Measuring point 4, 213, is connected to measuring point 5, 215, throughon and off switch 3, 305.

Measuring points 6, 1, 3, 4, 5, 2, and 0, 325, 208, 211, 213, 215, 320,and 319, respectively, inside of the device for body composition andhydration status analysis 327, are connected through on and off switches7-15, 312, 313, 314, 315, 316, 317, 322, 310, and 323, respectively.Measuring point 0, 319, is connected to earth potential 202. Measuringpoint 6, 325, is connected to measuring point 0, 319, through referenceresistance 1, 324, and on and off switch 8, 313. Measuring point 6, 325,is also connected to earth potential 202 through on and off switch 15,323. Measuring point 1, 208, is connected to measuring point 0, 319,through on and off switch 14, 310, and on and off switch 8, 313.Measuring point 3, 211, is connected to measuring point 0, 319, throughon and off switch 9, 314. Measuring point 4, 213, is connected tomeasuring point 0, 319, through on and off switch 10, 315. Measuringpoint 5, 215, is connected to measuring point 0, 319, through on and offswitch 11, 316. Measuring point 2, 320, is connected to measuring point0, 319, through on and off switch 12, 317.

FIG. 4. illustrates the measuring circuit of the first embodiment todetermine the impedance of a human subject at various frequencies. Themeasuring circuit consists of the following elements in this order:connecting element 427; M6 or measuring point 6, 325; connecting element428; reference resistance 1, 324; connecting element 429; M1 ormeasuring point 1, 208; connecting element 419; current excitationelectrode 1, 410; connecting element 420; impedance of the human subjectat various frequencies consisting of resistance and reactance, 105;connecting element 421; current excitation electrode 2, 408; connectingelement 422; M5 or measuring point 5, 215; connecting element 423;reference resistance 2, 321; connecting element 424; M2 or measuringpoint 2, 320; connecting element 425; current source 2, 404; connectingelement 426, which is also connected to earth potential 202; currentsource 1, 403; and again connecting element 427.

The current source driving means consists of a first in first out memory401 and a digital-analog converter 402, which are connected with eachother. The first in first out memory 401 is connected to themicrocontroller unit 412 also containing memory means and a six-channelprogrammable gain instrumentation amplifier and filtering circuit. Thedigital-analog converter 402 is connected 431 to current source 1, 403,and is also connected 430 to current source 2, 404.

M1 or measuring point 1, 208, is between reference resistance 1, 324,and current excitation electrode 1, 410, on the measuring circuit and isalso connected to M1 or measuring point 1 input 208 inside themicrocontroller unit 412. M2 or measuring point 2, 320, is betweencurrent source 2, 404, and reference resistance 2, 321, on the measuringcircuit and is also connected to M2 or measuring point 2 input 320inside the microcontroller unit 412. M3 or measuring point 3, 211, isconnected to voltage sensing electrode 1, 415, and is also connected toM3 or measuring point 3 input 211 inside the microcontroller unit 412.M4 or measuring point 4, 213, is connected to voltage sensing electrode2, 418, and is also connected to M4 or measuring point 4 input 213inside the microcontroller unit 412. M5 or measuring point 5, 215, isbetween current excitation electrode 2, 408, and reference resistance 2,321, on the measuring circuit and is also connected to M5 or measuringpoint 5 input 215 inside the microcontroller unit 412. M6 or measuringpoint 6, 325, is between reference resistance 1, 324, and current source1, 403, on the measuring circuit and is also connected to M6 ormeasuring point 6 input 325 inside the microcontroller unit 412.

Voltage sensing electrode 1, 415, is between the human subject with itsimpedance at various frequencies 105 and M3 or measuring point 3, 211.Voltage sensing electrode 2, 418, is between the human subject with itsimpedance at various frequencies 105 and M4 or measuring point 4, 213.M0 or measuring point 0 input 319 inside the microcontroller unit 412 isconnected to earth potential 202. The digital signal processor unit ofthe device for body composition and hydration status analysis 413 isconnected to the microcontroller unit 412.

The overview of the operation of the first embodiment of the apparatusand method for the analysis of change of body composition and hydrationstatus and for dynamic indirect individualized measurement of componentsof the human energy metabolism is depicted in FIGS. 1A and 1B. AppendixA lists the definitions of the upper indices, definitions of lowerindices, signs for the estimated value and assigned variable, scalarvariables, vector variables, matrix variables, dynamic system andprocess models, measurement models, and model constants and definitionsused in my first embodiment.

The human subject's metabolism 105 takes up energy in the form of theingested carbohydrate intake 102, fat intake 103, and protein intake 104on day k. The metabolism uses this energy intake; the human subject 105undergoes body composition change of his or her glycogen store, fatstore, and protein store on an examined day k; and a total energyexpenditure 101 is produced. The embodiment of the apparatus for theanalysis of change of body composition and hydration status 109 measuresresistance directly at multiple frequencies and extrapolates indirectlyto zero frequency and an extrapolated infinite frequency on day k 106.Using these results the same device 109 measures the extracellular watermass 126, the intracellular water mass 127, the change of lean bodymass, and change of fat mass on day k 107. The extracellular water massand intracellular water mass 107 are calculated as in Eq. 148. and Eq.149., respectively, in process 30, FIG. 5L. The change of lean body massand change of body fat mass 107 are calculated as in Eq. 152. and Eq.153., respectively, in process 30, FIG. 5L. The same device 109 canoptionally measure acute change of extracellular water mass andintracellular water mass 108. The acute change of extracellular andintracellular water mass 108 are calculated as in Eq. 163. and Eq. 164.,respectively, in process 34, FIG. 5N. A measurement of physical activityenergy expenditure 110 is required on day k. Optional measurements ofingested energy in the form of carbohydrate 111, fat 112, and protein113 are taken on day j for calibration purposes. An optional measurementof resting metabolic rate 114 is taken on day j for calibrationpurposes. An optional measurement of nitrogen excretion 115 is taken onday j for calibration purposes to indirectly measure dailygluconeogenesis. An optional measurement of the rate of endogenouslipolysis 116 is taken on day j for calibration purposes to indirectlymeasure daily lipolysis. The method for dynamic indirect individualizedmeasurement of components of the human energy metabolism 130 comprises aSelf-Correcting Model of the Utilized Energy Intake 131, a Self-AdaptiveModel of the Human Energy Metabolism 132, and a calculation of thecomponents of the human energy metabolism 133. The Self-Correcting Modelof the Utilized Energy Intake 131 estimates the utilized energy intake,defined as the daily utilized energy of carbohydrate, fat, and proteincaloric intake 119. The Self-Adaptive Model of the Human EnergyMetabolism 132 estimates the daily change of body composition, definedas the change of glycogen store, fat store, and protein store 118. Thecalculation of the components of the human energy metabolism 133provides the macronutrient oxidation rate results, defined as the dailyrate of carbohydrate oxidation, fat oxidation, and protein oxidation120; daily resting metabolic rate 121; daily unknown forms of energylosses or gains 122; daily rate of endogenous lipolysis 123; dailynitrogen excretion 124; and daily gluconeogenesis from protein 125.

The overview of the operation of an embodiment of the apparatus for theanalysis of change of body composition and hydration status 109 isdepicted on FIG. 2, FIG. 3, and FIG. 4. The passive circuit elements ofthe Cole circuit model representing the impedance of the human subject105 is measured. The Cole circuit model consists of a resistance at anestimated zero frequency 205 connected parallel to the seriallyconnected membrane capacitance 207 and resistance at an extrapolatedinfinite frequency 206. At an estimated zero frequency, the Cole circuitmodel consists of a resistance at the estimated zero frequency 205 andat an extrapolated infinite frequency it reduces to a parallel circuitof a resistance at the estimated zero frequency 205 connected parallelto a resistance at the extrapolated infinite frequency 206. For higherfrequencies than zero and lower frequencies than an extrapolatedinfinite frequency, the Cole circuit model has properties of a compleximpedance with a resistance and reactance value. I perform measurementsat a multitude of discrete preset frequencies from 1 kilohertz to 1megahertz. At these frequencies, the presence of a membrane capacitance207 is also measurable and 205, 206, and 207 is detected as a specificresistance and reactance value of an impedance 105. For each presetfrequency, a particular impedance is found. The digital signal processorunit 413 calculates 205 and 206 by fitting the Cole circuit model to themeasured impedance values. In the measuring environment, other passiveelements with electrical properties are present as well. These are thestray capacitance 1, 204, the stray capacitance 2, 203 the excitationelectrode resistance 1, 209, the excitation electrode resistance 2, 214,the sensory electrode resistance 1, 210, and the sensory electroderesistance 2, 212. To determine the value of the unknown circuitelements, an excitation current of sinusoidal form flows through theunknown circuit elements and the voltage signal measurements are takenat the same time at six measuring points 208, 320, 211, 213, 215, and325. The excitation current comes from current sources 1 and 2, 403 and404, where one of the two current sources injects the excitation currentand the other sinks the current. The injecting and sinking functionalternates between the current sources 403 and 404 every half period ofthe excitation frequency. The voltage signal is measured along the pathof the measuring circuit, which starts off at earth potential 202,continues with 426, 403, 427, 325, 428, 324, 429, 208, 419, 410, 420,209, and 216, branches off to 204, 202, 222, 205, and 221, and 218, 207,219, 206, 205, and 220, merges at 217, branches off to 203, 202, 214,421, 408, 422, 215, 423, 321, 424, 320, 425, 404, and ends at 202. Aninput logic circuit 327 and 328 is used to isolate or short circuit orleave unchanged preselected parts of the measurement circuit. Thedetermination of the unknown lumped passive elements 105, 203, 204, 209,210, 212, and 214 occurs with appropriate setting of the input logiccircuit 327 and 328. Before each measurement cycle both offset voltageand voltage noise at six measuring points 208, 320, 211, 213, 215, and325 are measured. These results are used later for elimination of offseterror and minimization of voltage noise. The measurement cycle has twosteps. With step one, the following are determined: the value of straycapacitance 1, 204, excitation electrode resistance 1, 209, sensoryelectrode resistance 1, 210, stray capacitance 2, 203, excitationelectrode resistance 2, 214, and sensory electrode resistance 2, 212,using the input logic circuit 328 and 327 with appropriate setting ofswitches 1-15, 306, 307, 305, 309, 308, 311, 312, 313, 314, 315, 316,317, 322, 310, and 323, respectively, and applying Ohm's law andKirchhoff's first and second law.

In the second step, the following are determined: the unknown impedanceor resistance and reactance of the human subject 105 at a presetfrequency by using the input logic circuit 328 and 327 with appropriatesetting of switches 1-15, 306, 307, 305, 309, 308, 311, 312, 313, 314,315, 316, 317, 322, 310, and 323, respectively, and applying Ohm's lawand Kirchhoff's first and second law. The magnitude of the offsetvoltage and amplitude as well as the phase angle of the voltage signalfrom measuring point 6, 326, measuring point 1, 208, and measuring point3, 211, are referenced to reference resistance 1, 324, and frommeasuring point 2, 320, measuring point 5, 215, and measuring point 4,213, are referenced to reference resistance 2, 321, respectively.

The measurement of resistance and reactance of the human subject at eachpreset frequency starts with loading a sine function of at least 16 wavelengths to a first in first out memory 401 by a microcontroller unit412. Upon a trigger by the microcontroller unit 412, the train of atleast 16 sine waves is sent to a digital-analog converter 402 at apredetermined rate by the microcontroller unit 412. The digital-analogconverter 402 generates an excitation pattern with opposing phase forcurrent source 1, 403, and current source 2, 404. Programmable gaininstrumentation amplifiers within the microcontroller unit 412 pick upthe voltage signals at the six measuring points 208, 320, 211, 213, 215,and 325 and amplify and filter the signal adjusted by themicrocontroller within the microcontroller unit 412. The microcontrollerunit 412 performs analog-digital conversion of the amplified andfiltered voltage signal from the six measuring points 208, 320, 211,213, 215 and 325. The microcontroller unit 412 then sends the signalfirst to the memory means of the microcontroller unit 412 and upondemand sends the signal to a digital signal processor unit 413. Thedigital signal processor unit 413 uses a sine wave function fittingalgorithm to determine amplitude, phase, and offset of the digitized,amplified, and filtered voltage signal from the six measuring points208, 320, 211, 213, 215 and 325 by minimizing the sum of the square ofthe deviations between the measured signal and a mathematical sinefunction of known frequency. The errors of the filtered voltage signal,defined as the difference between the predicted and measureddigitalized, amplified, and filtered voltage signal from the sixmeasuring points 208, 320, 211, 213, 215 and 325, are used formeasurement of quality and to indicate whether a repeat measurementcycle is needed.

The digital processor unit 413 performs a non-linear curve fittingalgorithm of the Cole circuit model to the measured resistances andreactances of human subject 105 at preset frequencies and extrapolatesthe best fitting Cole circuit model curve to zero and an extrapolatedinfinite frequency to obtain resistance of the human subject at zero andan extrapolated infinite frequency. The sum of the square of thedeviations between Cole circuit model predicted and actually measuredimpedance values is used to measure quality and reliability of myapparatus' functioning.

FIG. 5A shows the detailed overview of the operation of the first methodfor the analysis of change of body composition and hydration status andfor dynamic indirect individualized measurement of components of thehuman energy metabolism. The method starts at 1. The calculation forsubsequent days merges with the start at 2. The algorithm branches offat decision point 3.

If this is an initiation day then the process continues at 5. The indexvariable for the day k is set to zero as expressed in Eq. 0. The initialvalues are entered for body cell mass BCM₀, extracellular water massECW₀, lean body mass L₀, intracellular water mass ICW₀, glycogen massG₀, fat mass F₀, protein mass P₀, ingested carbohydrate intakeCI^({tilde over (0)}), ingested fat intake FI_({tilde over (0)}),ingested protein intake PI_({tilde over (0)}), estimated correctionfactor for de novo lipogenesis {circumflex over (μ)}₀, estimatedcorrection factor for gluconeogenesis from amino acids {circumflex over(ν)}₀, and estimated correction factor for unidentified energy losses orgains {circumflex over (φ)}₀.

If this is not an initiation day then the process continues at 4 wherethe index variable for day k is set to a chosen value.

The algorithm branches off at decision point 6.

If this is a calibration day and the ingested macronutrient calories areavailable, the process continues at 7 with Eq. 1. to Eq. 3, whichcalculate the utilized macronutrient energy intake vector²⁷ from theingested macronutrient intake. ²⁷ Hall, DOI: 10.1152/ajpendo.00559.2009

The algorithm branches off at decision point 600.

If a calculation with canonical representation using the R-ratio ischosen then the process will continue with an R-ratio method using aCanonical Model Form of the Human Energy Metabolism method. The seriallymeasured lean body mass L′_(k) and fat mass F′_(k), is used throughoutthis algorithm where k runs from zero to the last day or day k. Themeasured values can come directly from process 19 or can be the resultof smoothing as in process 24 or the result of a trajectory calculationas in process 25.

At decision point 601, the process branches off.

If the estimation of the R-ratio will be with fixed {circumflex over(α)}₀=10400, then the process continues at process 602. The goal is tofind the best R-ratio estimate {circumflex over (R)}_(k) which wouldachieve the closest approximation of the vector with elements of dailylean body mass changes DL′_(k) to the product of R-ratio estimate{circumflex over (R)}_(k) and vector with elements of daily fat masschanges DF′_(k) with lowest sum of squared errors as in Eq. 200. Thevector with elements of daily lean body mass changes DL′_(k) is definedin Eq. 201 and the vector with elements of daily fat mass changesDF′_(k) is defined in Eq. 202. This estimation with minimum least squareerror can be done as in Eq. 203 or using the data recursive least squareestimation as in Eq. 204. The Kalman gain KR_(k) for R-ratio iscalculated as in Grewal.²⁸ The indirectly calculated estimation R-ratio{circumflex over (R)}_(k−1)* is calculated as in Eq. 205. The processcontinues with decision point 604. ²⁸ Grewal M. S. and A. P. Andrews.Kalman Filtering: Theory and Practice Using MATLAB. John Wiley & Sons,New Jersey. Third Ed.; Sept. 2011, 136 pp.

If the estimation of the R-ratio will be with slowly drifting{circumflex over (α)}_(k) on day k then the process continues at process603. The goal is to find the best R-ratio estimate {circumflex over(R)}_(k) which would achieve the closest approximation of the vectorwith elements of daily lean body mass LL′_(k) to the product of vectorwith elements of the natural logarithm of the daily fat mass LF′_(k) andthe parameter vector of the lean body mass-fat mass interrelationship{circumflex over (p)}_(k) as in Eq. 206. The vector with elements ofdaily lean body mass LL′_(k) is defined in Eq. 207 and the vector withelements of the natural logarithm of the daily fat mass LF′_(k) isdefined in Eq. 208. The vector parameter of lean body mass-fat massinterrelationship {circumflex over (p)}_(k) is defined in Eq. 206a. Theestimation of {circumflex over (p)}_(k)with minimum least square errorcan be done as in Eq. 209 or using the data recursive least squareestimation as in Eq. 210. The Kalman gain matrix Kp_(k) is calculated asin Grewal.²⁹ The calculation of the parameter vector of the lean bodymass-fat mass inter relationship p_(k)* on day k is in Eq. 211.{circumflex over (R)}_(k) is estimated in Eq. 212. The process continueswith decision point 604. ²⁹ Grewal M. S. and A. P. Andrews. KalmanFiltering: Theory and Practice Using MATLAB. John Wiley & Sons, NewJersey. Third Ed.; September 2011, 136 pp.

The algorithm branches off at decision point 604.

If individualized estimation of daily energy density of the lean bodymass change ρ_(L) _(k) and daily energy density of the fat mass changeρ_(F) _(k) is needed, then the process continues at 606. Here thecoefficient of daily energy balance and lean mass changeinterrelationship Â_(k) and the coefficient of daily energy balance andfat mass change interrelationship {circumflex over (B)}_(k) areestimated with the goal of error least square for Â_(k) as in Eq. 215and for {circumflex over (B)}_(k) as in Eq. 216. The definition of thevector with elements of daily energy balance values DIO′_(k) is as inEq. 217. The definition of the vector with elements of daily lean bodymass changes DL′_(k) is as in Eq. 218. The definition of the vector withelements of daily fat mass changes DF′_(k) is as in Eq. 219. Theestimation of Â_(k) with minimum least square error can be done as inEq. 220a or using the data recursive least square estimation as in Eq.221. The Kalman gain KA_(k) is calculated as in Grewal.³⁰ The indirectlycalculated coefficient of daily energy balance and lean mass changeinterrelationship Â_(k)* is calculated as in Eq. 223. The estimation of{circumflex over (B)}_(k) with minimum least square error can be done asin Eq. 220b or using the data recursive least square estimation as inEq. 222. The Kalman gain KB_(k) is calculated as in Grewal.³¹ Theindirectly calculated coefficient of daily energy balance and lean masschange interrelationship {circumflex over (B)}_(k)* is calculated as inEq. 224. The indirectly calculated daily energy density of the fat masschange ρ_(F) _(k) * is calculated in Eq. 225a if there was a fat massgain on previous day or in Eq. 225b if there was no fat mass gain onprevious day. The indirectly calculated daily energy density of the leanbody mass change ρ_(L) _(k) * is calculated in Eq. 226. The estimateddaily energy density of the fat mass change {circumflex over (ρ)}_(F)_(k) is calculated in Eq. 227. The estimated daily energy density of thelean body mass change {circumflex over (ρ)}_(L) _(k) is calculated inEq. 228. The Kalman gains Kρ_(F) _(k) and Kρ_(L) _(k) are calculated asin Grewal.³² The process continues with decision point 607. ³⁰ Id.³¹Id.³² Id.

If individualized estimation of daily energy density of the lean bodymass change {circumflex over (ρ)}_(L) _(k) and daily energy density ofthe fat mass change {circumflex over (ρ)}_(F) _(k) are not needed, thenthe process continues with 605 and ρ_(L) _(k) takes up its default valueas in Eq. 213 and ρ_(F) _(k) takes up its default value as in Eq. 214.The process continues with decision point 607.

At process 607 the gluconeogenesis from protein is calculated with Eq.229-Eq. 233. In the next process step 608 the macronutrient oxidationsare calculated. The protein oxidation is calculated in Eq. 234 using theprotein mass indirectly calculated with measured values ΔP_(k+1)*′. Thedaily change ΔP_(k+1)*′ is calculated in Eq. 235. The rate of fatoxidation is calculated in Eq. 236. The rate of carbohydrate oxidationis calculated in Eq. 237. In the next process 609 the energy flux fromcarbohydrate pool to fat pool {circumflex over (σ)}_(k) is estimated asin Eq. 238. The indirectly calculated parameter for energy flux fromcarbohydrate pool to fat pool σ_(k)* is calculated as in in Eq. 239. TheKalman gain Kσ_(k) is calculated as in Grewal.³³ In the next process 610the estimation of parameter for uncounted energy {circumflex over(ω)}_(k) is performed as in Eq. 240. The indirectly calculated parameterfor uncounted energy ω_(k)* is calculated as in Eq. 241. The Kalman gainKω_(k) is calculated as in Grewal.³⁴ In the next process 611 theSelf-Adaptive Input Output Model of the Human Energy Metabolism(SIO-HEM) is shown. In Eq. 242 the daily change of the lean bodyΔL_(k+i) mass is calculated. In Eq. 243 the daily change of the fat massΔF_(k+1) is calculated. In Eq. 244 the daily change of the protein massΔP_(k+1) is calculated. In the next process 612 the estimator equationsof the Self-Adaptive Input Output Model of the Human Energy Metabolism(SIO-HEM) are shown. In Eq. 245 estimated daily change of the lean bodymass at end of day k Δ{circumflex over (L)}_(k+1) is calculated. In Eq.246 estimated daily change of the fat mass at end of day k Δ{circumflexover (F)}_(k+1) is calculated. In Eq. 247 estimated daily change of theprotein mass at end of day k Δ{circumflex over (P)}_(k+1) is calculated.In Eq. 248 the deviation of estimated lean body mass from measured leanbody mass δL_(k) is calculated. In Eq. 249 the deviation of estimatedfat mass from measured fat mass δF_(k) is calculated. In Eq. 250 thedeviation of estimated protein mass from measured protein δP_(k) mass iscalculated. In Eq. 251 the protein mass indirectly calculated withmeasured values P_(k)*′ is calculated. ³³ Id.³⁴ Id.

In the next process 613 the Canonical Model Form of the Human EnergyMetabolism (C-HEM) is shown. In Eq. 252 the lean body mass L_(k+1) atthe end of day k is calculated. In Eq. 253 the fat mass F_(k+1) at theend of day k is calculated. In Eq. 254 the protein mass P_(k+1) at theend of day k is calculated. In the next process 614 the estimatorequations of the Canonical Model Form of the Human Energy Metabolism(C-HEM) are shown. In Eq. 255 the estimation of the lean body mass{circumflex over (L)}_(k+1) at the end of day k is calculated. In Eq.256 the estimation of fat mass {circumflex over (F)}_(k+1) at the end ofday k is calculated. In Eq. 257 the estimation of protein mass{circumflex over (P)}_(k+1) at the end of day k is calculated.

In the next process 615 inverse calculation of utilized macronutrientintake using trajectory values of the body composition changes is shown.In matrix equation Eq. 258 the estimated utilized carbohydrate intake

_(k), the estimated utilized fat intake

_(k), and the estimated utilized protein intake

_(k) are calculated from known change of lean body mass trajectory onday k ΔL*_(k+1) ^(TR), change of fat mass trajectory on day k ΔF*_(k+1)^(TR), and change of protein mass trajectory on k ΔP*_(k+1) ^(TR). Thetrajectory values can come from indirectly measured data as generated byprocess 19 as indicated in Eq. 260 or can be the result of smoothing asin process 24 or trajectory calculation as process 25. The indirectlymeasured Nexcr*′_(k) can be calculated as in Eq. 259.

The process continues at 44. If at decision point 600 no calculationwith canonical representation using the R-ratio is chosen, then theprocess continues at 9.

At process 9, Eq. 4. calculates the rate of proteolysis and Eq. 5.calculates the rate of glycogenolysis. Eq. 6. calculates the fat storedependent coefficient for rate of endogenous lipolysis on day k. Eq. 7.calculates the carbohydrate intake dependent coefficient for rate ofendogenous lipolysis. Eq. 8. calculates the bias for rate of endogenouslipolysis on day k. Eq. 9. calculates the rate of endogenous lipolysison day k. Eq. 10. calculates the carbohydrate intake dependentcoefficient for rate of de novo lipogenesis. Eq. 11. calculates theglycogen store dependent coefficient for rate of de novo lipogenesis onday k. Eq. 12. calculates bias for rate of endogenous lipolysis on dayk. Eq. 13. calculates the rate of de novo lipogenesis. Eq. 14.calculates the rate of glycerol gluconeogenesis. Eq. 15. calculates theprotein store dependent coefficient for gluconeogenesis from protein.Eq. 16. calculates the carbohydrate intake dependent coefficient forgluconeogenesis from protein. Eq. 17. calculates the protein intakedependent coefficient for gluconeogenesis from protein. Eq. 18.calculates the bias for gluconeogenesis from protein. Eq. 19. calculatesthe rate of gluconeogenesis from protein. Eq. 20. calculates theglycerol 3-phosphate synthesis. Eq. 21. calculates the resting metabolicrate with a filtering formula on day k. Eq. 22. calculates theindirectly calculated total energy expenditure from the restingmetabolic rate with the filtering formula on day k and directly measuredphysical activity energy expenditure. Eq. 23. calculates the 24 hournitrogen excretion from utilized protein intake on day k and the dailychange of the protein store for day k−1. The process continues at 16.

If at decision point 6 this is not a calibration day and the ingestedmacronutrient calories are not available, the process continues atdecision point 8.

If there is no trajectory value ΔBC_(k+1) ^(TR)*, called the change oftrajectory of indirectly calculated change of body composition vector ofday k, available for ΔBC_(k+1)*, called the indirectly calculated changeof body composition vector of day k, at decision point 8, then thealgorithm continues with process 10.

At process 10, Eq. 24. shows the calculation of the rate of proteolysison day k. Eq. 25. calculates the rate of glycogenolysis on day k. Eq.26. calculates the fat store dependent coefficient for the rate ofendogenous lipolysis on day k. Eq. 27. calculates the carbohydrateintake dependent coefficient for the rate of endogenous lipolysis on dayk. Eq. 28. calculates the bias for the rate of endogenous lipolysis onday k. Eq. 29. calculates the rate of endogenous lipolysis on day k. Eq.30. calculates the carbohydrate intake dependent coefficient for therate of de novo lipogenesis on day k. Eq. 31. calculates the glycogenstore dependent coefficient for the rate of de novo lipogenesis on dayk. Eq. 32. calculates the bias for the rate of endogenous lipolysis onday k. Eq. 33. calculates the rate of de novo lipogenesis on day k. Eq.34. calculates the rate of glycerol gluconeogenesis on day k. Eq. 35.calculates the protein store dependent coefficient for gluconeogenesisfrom protein on day k. Eq. 36. calculates the carbohydrate intakedependent coefficient for gluconeogenesis from protein on day k. Eq. 37.calculates the protein intake dependent coefficient for gluconeogenesisfrom protein on day k. Eq. 38. calculates the bias for gluconeogenesisfrom protein on day k. Eq. 39. calculates the rate of gluconeogenesisfrom protein on day k. Eq. 40. calculates a part of the restingmetabolic rate which is independent of the body composition vectorchanges and the time-varying constant energy expenditure on day k. Eq.41. calculates the resting metabolic rate with predictive formula on dayk. Eq. 42. calculates a part of the resting metabolic rate which isdependent on the utilized carbohydrate intake on day k. Eq. 43.calculates a part of the resting metabolic rate which is dependent onthe utilized fat intake on day k. Eq. 44. calculates a part of theresting metabolic rate which is dependent on the utilized protein intakeon day k. The process continues at 11.

At process 11, Eq. 45. constructs the energy constant matrix of theRetained or Released Energy Model of the Human Energy Metabolism on dayk. Eq. 46. constructs the time varying utilized energy intake couplingmatrix in the Retained or Released Energy Model of the Human EnergyMetabolism on day k. Eq. 47. constructs the indirectly calculated biasvector of the Retained or Released Energy Model of the Human EnergyMetabolism on day k. Eq. 48. calculates the utilized energy intakevector indirectly with the Measurement Model of the Utilized EnergyIntake from body composition vector change on day k, which I obtaineither from Eq. 117. or Eq. 119. where I obtain the lean body masschange and fat mass change from 107, which is part of 109, the deviceand method for body composition and hydration status analysis. Eq. 49.assigns the value of the utilized carbohydrate intake indirectlycalculated by the Measurement Model of the Utilized Energy Intake frombody composition vector change on day k to the variable for the utilizedcarbohydrate intake on day k. Eq. 50. assigns the value of the utilizedfat intake indirectly calculated by the Measurement Model of theUtilized Energy Intake from body composition vector change on day k tothe variable for the utilized fat intake on day k. Eq. 51. assigns thevalue of the utilized protein intake indirectly calculated by theMeasurement Model of the Utilized Energy Intake from body compositionvector change on day k to the variable for the utilized protein intakeon day k. The process continues at process 9.

If there is a trajectory value ΔBC_(k+1) ^(TR)*, called the change oftrajectory of indirectly calculated change of body composition vector ofday k, available for ΔBC_(k+1)*, called the indirectly calculated changeof body composition vector of day k, at decision point 8, then thealgorithm continues with process 12.

At process 12, Eq. 52. shows the calculation of the rate of proteolysison day k−1. Eq. 53. calculates the rate of glycogenolysis on day k−1.Eq. 54. calculates the fat store dependent coefficient for the rate ofendogenous lipolysis on day k−1. Eq. 55. calculates the carbohydrateintake dependent coefficient for the rate of endogenous lipolysis on dayk−1. Eq. 56. calculates the bias for the rate of endogenous lipolysis onday k−1. Eq. 57. calculates the rate of endogenous lipolysis on day k−1.Eq. 58. calculates the carbohydrate intake dependent coefficient for therate of de novo lipogenesis on day k−1. Eq. 59. calculates the glycogenstore dependent coefficient for the rate of de novo lipogenesis on dayk−1. Eq. 60. calculates the bias for the rate of endogenous lipolysis onday k−1. Eq. 61. calculates the rate of de novo lipogenesis on day k−1.Eq. 62. calculates the rate of glycerol gluconeogenesis on day k−1. Eq.63. calculates the protein store dependent coefficient forgluconeogenesis from protein on day k−1. Eq. 64. calculates thecarbohydrate intake dependent coefficient for gluconeogenesis fromprotein on day k−1. Eq. 65. calculates the protein intake dependentcoefficient for gluconeogenesis from protein on day k−1. Eq. 66.calculates the bias for gluconeogenesis from protein on day k−1. Eq. 67.calculates the rate of gluconeogenesis from protein on day k−1. Eq. 68.calculates a part of the resting metabolic rate which is independent ofthe body composition vector changes and the time-varying constant energyexpenditure on day k−1. Eq. 69. calculates the resting metabolic ratewith predictive formula on day k−1. Eq. 70. calculates a part of theresting metabolic rate which is dependent on the utilized carbohydrateintake on day k−1. Eq. 71. calculates a part of the resting metabolicrate which is dependent on the utilized fat intake on day k−1. Eq. 72.calculates a part of the resting metabolic rate which is dependent onthe utilized protein intake on day k−1. The process continues at 13.

At process 13, Eq. 73. shows the calculation of rate of proteolysis onday k. Eq. 74. calculates the rate of glycogenolysis on day k. Eq. 75.calculates the fat store dependent coefficient for rate of endogenouslipolysis on day k. Eq. 76. calculates carbohydrate intake dependentcoefficient for rate of endogenous lipolysis on day k. Eq. 77.calculates the bias for rate of endogenous lipolysis on day k. Eq. 78.calculates the rate of endogenous lipolysis on day k. Eq. 79. calculatesthe carbohydrate intake dependent coefficient for the rate of de novolipogenesis on day k. Eq. 80. calculates the glycogen store dependentcoefficient for the rate of de novo lipogenesis on day k. Eq. 81.calculates the bias for the rate of endogenous lipolysis on day k. Eq.82. calculates the rate of de novo lipogenesis on day k. Eq. 83.calculates the rate of glycerol gluconeogenesis on day k. Eq. 84.calculates the protein store dependent coefficient for gluconeogenesisfrom protein on day k. Eq. 85. calculates the carbohydrate intakedependent coefficient for gluconeogenesis from protein on day k. Eq. 86.calculates the protein intake dependent coefficient for gluconeogenesisfrom protein on day k. Eq. 87. calculates the bias for gluconeogenesisfrom protein. Eq. 88. calculates the rate of gluconeogenesis fromprotein on day k. Eq. 89. calculates a part of the resting metabolicrate that is independent of the body composition vector changes and thetime-varying constant energy expenditure on day k. Eq. 90. calculatesthe resting metabolic rate with a predictive formula on day k. Eq. 91.calculates a part of the resting metabolic rate which is dependent onthe utilized carbohydrate intake on day k. Eq. 92. calculates a part ofthe resting metabolic rate which is dependent on the utilized fat intakeon day k. Eq. 93. calculates a part of the resting metabolic rate whichis dependent on the utilized protein intake on day k. The processcontinues at 14.

At process 14, Eq. 94. constructs the time varying utilized energyintake coupling matrix in the Retained or Released Energy Model of theHuman Energy Metabolism on day k−1. Eq. 95. constructs the indirectlycalculated bias vector of the Retained or Released Energy Model of theHuman Energy Metabolism on day k−1. Eq. 96. constructs the time varyingutilized energy intake coupling matrix in the Retained or ReleasedEnergy Model of the Human Energy Metabolism on day k. Eq. 97. constructsthe indirectly calculated bias vector of the Retained or Released EnergyModel of the Human Energy Metabolism on day k. Eq. 98. calculates thedynamic transition matrix in the Self-Correcting Model of the UtilizedEnergy Intake on day k−1. Eq. 99. calculates dynamic coupling matrix inthe Self Corrective Model of the Utilized Energy Intake on day k−1. Eq.100. calculates the time varying bias vector in the Self CorrectiveModel of the Utilized Energy Intake on day k−1. Eq. 101. calculates theutilized energy intake vector, with the elements consisting of the dailymetabolized macronutrient intake from carbohydrate, fat and protein onday k. I refer to Eq. 101. as the Linear Model of the Utilized EnergyIntake, and this linear model also serves as the process model of theSelf-Correcting Model of the Utilized Energy Intake. Eq. 102. calculatesthe indirectly measured utilized energy intake vector on day k using theRetained or Released Energy Model of the Human Energy Metabolism, and Irefer to Eq. 102. as the Measurement Model of the Utilized Energy Intakefrom body composition vector change. The input variable to Eq. 102. isthe indirectly calculated change of body composition vector of day k,which I obtain either from Eq. 117. or Eq. 119. where the lean body masschange and fat mass change from 107 are obtained, which is part of 109,the device and method for body composition and hydration statusanalysis. The process continues at process 15.

At process 15, the deviation of the estimated indirectly calculatedutilized energy intake vector is evaluated with one of two optionalequations, Eq. 103. or Eq. 104. Eq. 103. calculates the deviation of theestimated indirectly calculated utilized energy intake vector from theindirectly measured utilized energy intake vector on day k using theindirectly calculated change of body composition vector of day k and theMeasurement Model of the Utilized Energy Intake. Eq. 104. calculates thedeviation of the estimated indirectly calculated utilized energy intakevector from a trajectory using the change of trajectory of indirectlycalculated change of body composition vector of day k and theMeasurement Model of the Utilized Energy Intake. Eq. 105. implements thediscrete time Kalman estimator with innovations representation for thedaily utilized macronutrient energy intake vector using theSelf-Correcting Model of the Utilized Energy Intake with innovationsrepresentation. The Kalman gain matrix is calculated as in Grewal,(Grewal M. S. and A. P. Andrews. Kalman Filtering: Theory and PracticeUsing MATLAB. John Wiley & Sons, New Jersey. Third Ed.; September 2011,136 pp.). Eq. 106. assigns the estimated indirectly calculated utilizedenergy intake vector by the Self-Correcting Model of the Utilized EnergyIntake on day k to the utilized energy intake vector with elements ofdaily metabolized macronutrient intake of carbohydrate, fat, and proteinon day k. The process continues at 9.

At process 16, the macronutrient oxidation rates are calculated. Eq.107. constructs the oxygen caloric heat equivalent constants matrix. Eq.108. constructs the indirectly calculated heat energy equivalent vectoron day k. Eq. 109. calculates the indirectly calculated macronutrientoxidation vector with the elements of energy content obtained afteroxidation of carbohydrate, fat, and protein on day k. Eq. 110. assignsthe values of the components of the macronutrient oxidation vector tovariables of the calculated rate of carbohydrate oxidation, calculatedrate of fat oxidation, and calculated rate of protein oxidation. Theprocess continues at 17.

The process at 17 shows the process model of the Linear Extended Modelof the Human Energy Metabolism. Eq. 111. calculates the daily energy ofthe glycogen store change for day k. Eq. 112. calculates the dailyenergy of fat store change for day k. Eq. 113. calculates the dailyenergy of protein store change for day k. The calculations in Eq. 111.to Eq. 113. are represented also in Eq. 114. with a matrixrepresentation to calculate the change of body composition vector at theend of day k.

The algorithm branches off at decision point 18 and reunites again at21. The measurement model can be either the Measurement Model of BodyComposition Change from Lean-Fat-Protein as in Eq. 115. to Eq. 117. atprocess 19 or the Measurement Model of Body Composition Change fromLean-Fat-Resting Metabolic Rate as in Eq. 118. to Eq. 119. at process20. Eq. 115. calculates daily change of the indirectly calculated bodyprotein mass on day k. Eq. 116. calculates the change of the indirectlycalculated lean-fat-protein vector of day k. Eq. 117. calculates theindirectly calculated change of body composition vector for day k, whereI obtain the lean body mass change and fat mass change from 107, whichis part of 109, the device and method for body composition and hydrationstatus analysis. I refer to Eq. 117 as the Measurement Model of BodyComposition Change from Lean-Fat-Protein. The algorithm continues at 21.

At process 20, Eq. 118 is the change of the indirectly calculatedlean-fat-resting-metabolic-rate vector of day k. Eq. 119 calculates theindirectly calculated change of body composition vector for day k whereI obtain the lean body mass change and fat mass change from 107, whichis part of 109, the device and method for body composition and hydrationstatus analysis. I refer to Eq. 119. as the Measurement Model of BodyComposition Change from Lean-Fat-Resting-Metabolic-Rate. The algorithmcontinues at 21.

At process 21, the deviation of the estimated indirectly calculatedchange of body composition vector is evaluated with one of threeoptional equations, Eq. 120, Eq. 121, or Eq. 122. Eq. 120 calculates thedeviation of the estimated indirectly calculated change of bodycomposition vector of day k from the indirectly measured one using theMeasurement Model of Body Composition Change from Lean-Fat-Protein. Eq.121 calculates the deviation of the estimated indirectly calculatedchange of body composition vector of day k from the indirectly measuredone using the Measurement Model of Body Composition Change fromLean-Fat-Resting-Metabolic-Rate. Eq. 122 calculates the deviation of theestimated indirectly calculated change of body composition vector from atrajectory on day k. Eq. 123 implements the discrete time variant Kalmanestimator with innovations representation for the estimation of theindirectly calculated change of body composition of day k. In thisequation, I use the Self-Adaptive Model of the Human Energy Metabolismand innovations representation technique. The resulting estimates of thedaily body composition change of day k allow for stochasticidentification of the correction factors for de novo lipogenesis,gluconeogenesis from amino acids, and the correction factor forunidentified energy losses or gains, so that these model parametersbecome Self-Adaptive. The Kalman gain matrices are calculated as inGrewal.³⁵ The algorithm continues at 22. ³⁵ Grewal M. S. and A. P.Andrews. Kalman Filtering: Theory and Practice Using MATLAB. John Wiley& Sons, New Jersey. Third Ed.; September 2011, pp. 136

At process 22, the estimators for the correction factors for de novolipogenesis, gluconeogenesis from amino acids, and for unidentifiedenergy losses or gains are shown in Eq. 124 to Eq. 126 Eq. 124 sets thea posteriori estimation of the correction factor for de novo lipogenesisof day k equal to the a priori estimation of the correction factor forde novo lipogenesis of day k+1. Eq. 125 sets the a posteriori estimationof the correction factor for gluconeogenesis of day k equal to the apriori estimation of the correction factor for gluconeogenesis of dayk+1. Eq. 126 sets the a posteriori estimation of the correction factorfor unidentified energy losses or gains of day k equal to the a prioriestimation of the correction factor for unidentified energy losses orgains of day k+1. The measurement equations for the correction factorsfor de novo lipogenesis, gluconeogenesis from amino acids, and forunidentified energy losses or gains are calculated as in Eq. 127 to Eq.129. The a posteriori estimation of the correction factors for de novolipogenesis, gluconeogenesis from amino acids, and for unidentifiedenergy losses or gains is performed using the Kalman filter as in Eq.130 to Eq. 132. The Kalman gains are calculated as a scalar problem asin Grewal.³⁶ The algorithm continues at 23. ³⁶ Grewal M. S. and A. P.Andrews. Kalman Filtering: Theory and Practice Using MATLAB. John Wiley& Sons, New Jersey. Third Ed.; September 2011, pp. 140

The algorithm branches off at decision point 23.

If no calibrations are desired than the process continues at decisionpoint 26.

If this is a calibration day j with known ingested carbohydrate, fat,and protein calories; a known calibration value for body compositionvector; and a trajectory calculation for body composition vector changesis desired, then a smoothing procedure of the indirectly calculated bodycomposition vector change is performed and the process continues at 24.It may be preferable to use optimal smoothers.³⁷ The process continuesat 25. ³⁷ Grewal M. S. and A. P. Andrews. Kalman Filtering: Theory andPractice Using MATLAB. John Wiley & Sons, New Jersey. Third Ed.;September 2011, pp. 183

At process 25, the trajectory calculation is performed. My firstembodiment uses the smoothed values of the indirectly measured bodycomposition vector. The time interval for the trajectory is day i, whichis the day of the previous calibration, to day j, which is the day ofthe last calibration. The constraint is that the trajectory starts witha calibration value of day i and ends with a calibration value of day jfor the body composition vector. Eq. 133 calculate the trajectory of thebody composition vector from day i to day j using the results of thesmoothing algorithm. Alternative methods of trajectory creation includeusing mathematical methods³⁸ which express the function of thetrajectory as a parametric curve. Eq. 134 calculates the trajectory ofthe body composition vector from day i to day j using a polynomialspline function. Eq. 135 calculates the trajectory of the bodycomposition vector from day i to day j using a B spline function. Eq.136 calculates the trajectory of the body composition vector from day ito day j using a Bezier function. The algorithm continues at 26 andbranches off at decision point 26. If no calibrations for the adjustablecoefficients to calculate extracellular water and intracellular watermasses are needed, then the process continues at 29. ³⁸ Venkataraman, P.Applied Optimization with MATLAB Programming. March 2009; John Wiley &Sons, pp. 490

If a calibration procedure for the adjustable coefficients to calculateextracellular water and intracellular water masses is needed, then theprocess continues at 27 and reference values are generated first. Thereference value for extracellular water mass on calibration day j isobtained from tabled values³⁹ as shown in Eq. 137, where the values aredependent on weight, height, age, sex and race. The reference value forintracellular water mass on calibration day j is calculated in Eq.140.⁴⁰ The formula requires the body weight and the reference value forfat mass on calibration day j. The reference value for fat mass oncalibration day j is obtained from the anthropomorphic determination ofbody fat as in Lean⁴¹, as in Eq. 138 for men and Eq. 139 for women. Eq.141 calculates the reference value for the lean body mass. ³⁹ Silva,DOI:10.1088/0967-3334/28/5/004⁴⁰ Jaffrin, DOI:10.1016/j.medengphy.2008.06.009⁴¹ Lean, et al. Predicting bodycomposition vector by densitometry from simple anthropometricmeasurements. American Journal of Clinical Nutrition, January 1996;63(1): 4-14

The calibration process proceeds to 28, where the adjustablecoefficients to calculate extracellular water and intracellular watermasses are estimated. Eq. 142. sets the a posteriori estimation of theadjustable coefficient to calculate extracellular water on calibrationday i equal to the a priori estimation of the adjustable coefficient tocalculate extracellular water on day j. Eq. 143. sets the a posterioriestimation of the adjustable coefficient to calculate intracellularwater on calibration day i equal to a priori estimation of theadjustable coefficient to calculate intracellular water on day j. Themeasurement equations for the adjustable coefficients to calculateextracellular water and intracellular water masses are calculated as inEq. 144. to Eq. 145. The a posteriori estimation of the adjustablecoefficients to calculate extracellular water and intracellular watermasses is performed using the Kalman filter as in Eq. 146 and Eq. 147.The Kalman gains are calculated as a scalar problem as in Grewal.⁴² Thealgorithm continues at 29. ⁴² Grewal M. S. and A. P. Andrews. KalmanFiltering: Theory and Practice Using MATLAB. John Wiley & Sons, NewJersey. Third Ed.; September 2011, pp. 140

The algorithm branches off at decision point 29. If no measurement ofthe body composition vector and daily change in body composition vectoris needed, then the process continues at decision point 31.

If measurement of the body composition vector and daily change in bodycomposition vector is needed, then these can be calculated at process30. Eq. 148 calculates the extracellular water mass from the resistanceextrapolated at zero frequency. Eq. 149 calculates the intracellularwater mass from the resistance at an extrapolated infinite frequency.The lean body mass is calculated with Eq. 150.⁴³ The body fat mass isobtained by subtracting the lean body mass from body weight as in Eq.151. The lean body change from one day to the next day is obtained bysubtracting the previous day's lean body mass from the next day's leanbody mass as in Eq. 152. The daily fat mass change is obtained bysubtracting the daily change of lean body mass from the daily bodyweight change as in Eq. 153. The algorithm continues at 31. ⁴³ Jaffrin,DOI: 10.1016/j.medengphy.2008.06.009

The algorithm branches off at decision point 31. If no calibrationprocedure for the adjustable dynamic coefficients to calculateextracellular water and intracellular water mass changes is needed, thenthe process continues at decision point 33.

If a calibration procedure for the adjustable dynamic coefficients tocalculate extracellular water and intracellular water mass changes isneeded, then the process continues at 32.

At process 32, a calibration procedure is performed for the adjustabledynamic coefficients to calculate extracellular water mass andintracellular water mass changes. In calculating dynamic changes ofextracellular water and intracellular water, I take advantage of theobservation that the ratio of the extracellular and total body water istightly regulated in normal physiology.⁴⁴ The ratio can be calculateusing reference values on day j. The ratio of the extracellular andtotal body water is determined from reference extra cellular water andintracellular water mass as in Eq. 154. ⁴⁴ Ellis K J, Wong W W (1998)Human hydrometry: comparison of multifrequency bioelectrical impedancewith ²H₂O and bromine dilution. J Appl Physiol 85(3): 1056-1062

For the calibration of the acute change of extracellular andintracellular water mass, a known change of the total water mass isneeded in a relatively short period of time so as not to affect the bodycomposition vector change. Vigorous perspiration or rapid hydration withfluid can be such a sentinel event when the body loses or gains ameasurable weight in a short period of time without any significantchange of the body composition. The ensuing body weight change, andequivalently, the total body water change from the beginning to the endof the sentinel event causes the hydration change. The indirectlycalculated extracellular water change for this scenario can becalculated as in Eq. 155. Eq. 155 requires the knowledge of the totalwater change of the body which can be obtained by measuring the weightbefore and after a sentinel event and calculating the difference. Theensuing change of the intracellular water is calculated in Eq. 156. Eq.157 sets the a posteriori estimation of the adjustable dynamiccoefficient to calculate extracellular water on calibration day i equalto the a priori estimation of the adjustable dynamic coefficient tocalculate extracellular water on day j. Eq. 158 sets the a posterioriestimation of the adjustable dynamic coefficient to calculateintracellular water on calibration day i equal to the a prioriestimation of the adjustable dynamic coefficient to calculateintracellular water on day j. The measurement equations for theadjustable dynamic coefficients to calculate extracellular andintracellular water masses are calculated in Eq. 159 to Eq. 160. The aposteriori estimation of the adjustable dynamic coefficients tocalculate extracellular and intracellular water masses is performedusing the Kalman filter in Eq. 161 and Eq. 162 and the Kalman gains arecalculated as a scalar problem as in Grewal.⁴⁵ The algorithm continuesat decision point 33. ⁴⁵ Grewal M. S. and A. P. Andrews. KalmanFiltering: Theory and Practice Using MATLAB. John Wiley & Sons, NewJersey. Third Ed.; September 2011, page 140

The algorithm branches off at decision point 33. If no measurement ofacute change of hydration status is needed, then the process continuesat decision point 35.

If measurement for acute change of hydration status is needed, then theprocess continues at 34. Eq. 163 calculates dynamic changes ofextracellular water indirectly from resistance value changes before andafter the acute event causing hydration status change using theresistance extrapolated at zero frequency before and after a sentinelevent of hydration status change. Eq. 164 calculates dynamic changes ofintracellular water indirectly from resistance value changes before andafter the acute event causing hydration status change using theresistance at an extrapolated infinite frequency before and after asentinel event of hydration change. The process continues at decisionpoint 35 and branches off at decision point 35. If no calibrationprocedure for the estimation of the time varying constant energyexpenditure is needed, the process continues at 37.

If a calibration procedure for the estimation of the time varyingconstant energy expenditure is needed, then the process continues at 36.Eq. 165 sets the a posteriori estimation of the time varying constantenergy expenditure of the previous calibration day i equal to the apriori estimation of the time varying constant energy expenditure of thelast calibration day j. The measurement equation for the time-varyingconstant energy expenditure for calibration day j is calculated as inEq. 166. In this equation, the components of the indirectly calculatedbody composition vector change are entered, taken from the day beforethe calibration day j. Next, the a posteriori estimation of thetime-varying constant energy expenditure is performed using the Kalmanfilter as in Eq. 167, and the Kalman gains are calculated as a scalarproblem as in Grewal.⁴⁶ The process continues at decision point 37. ⁴⁶Id.

At decision point 37, if no calibration procedure for the basalgluconeogenesis rate is needed, the process continues at process 38. Ifa new value for the basal gluconeogenesis rate after previouscalibration on day j is available than an estimated gluconeogenesis fromprotein on day k with calibration can be calculated as in Eq. 170 bymultiplying the new value for the basal gluconeogenesis rate aftercalibration on day j with the estimation of the correction factor forgluconeogenesis from amino acids on day k and the gluconeogenesis fromprotein on day k and dividing the result with the old basalgluconeogenesis rate before calibration. The process continues atdecision point 40.

At decision point 37, if a calibration procedure for the basalgluconeogenesis rate is needed, then the process continues at 39. Forthis calibration procedure, the measured nitrogen excretion oncalibration day j is required. Eq. 168 calculates the indirectlymeasured correction factor for gluconeogenesis from amino acids oncalibration day j by evaluating a ratio with the numerator being theproduct of six point twenty-five multiplied with the energy density ofprotein and multiplied with the measured nitrogen excretion oncalibration day j minus the calculated rate of protein oxidation rate onday j, divided by the gluconeogenesis from protein on day j. Theindirectly measured correction factor for gluconeogenesis from aminoacids on calibration day j could be used for the process equation Eq.125 allowing for calibrated estimation of the gluconeogenesis fromprotein. Eq. 169 calculates the new value for the basal gluconeogenesisrate after previous calibration on day j by adding up the product of sixpoint twenty-five multiplied with the energy density of protein, andmultiplied with the measured nitrogen excretion on calibration day jminus the calculated rate of protein oxidation rate on day j. Theprocess continues at decision point 40.

At decision point 40, if no calibration procedure for baseline lipolysisrate is needed, then the process continues at 41. If a new value for thebaseline lipolysis rate after previous calibration on day j is availablethan an estimated rate of endogenous lipolysis on day k with calibrationcan be calculated as in Eq. 173 by multiplying the new value for thebaseline lipolysis rate after calibration on day j with the estimationof the correction factor for de novo lipogenesis on day k and the rateof endogenous lipolysis on day k and dividing the result by the oldbaseline lipolysis rate before calibration. The process continues atdecision point 43.

At decision point 40, if a calibration procedure for baseline lipolysisrate is needed, then the process continues at 42. For the calibrationprocedure, the measured rate of endogenous lipolysis on calibration dayj is required. Eq. 171 calculates the indirectly measured correctionfactor for de novo lipogenesis on calibration day j by calculating theratio of the baseline lipolysis rate before calibration and the measuredrate of endogenous lipolysis on calibration day j. The indirectlymeasured correction factor for de novo lipogenesis on calibration day jcould be used for the process equation Eq. 124 allowing for calibratedestimation of the rate of endogenous lipolysis. Eq. 172 calculates thenew value for the baseline lipolysis rate after previous calibration onday j by equating it with the the measured rate of endogenous lipolysison calibration day j. The process continues at decision point 43.

At process 43, preparations are made to proceed with calculations forthe next day. Eq. 173. increases the index variable for day k by one.Eq. 174 calculates the time-varying constant energy expenditure on dayk+1.

At process 44, the entire calculation for the next day can be performedby proceeding from 44 to 2.

Thus, at least one embodiment of the apparatus and method for theanalysis of the change of body composition and hydration status and fordynamic indirect individualized measurement of components of the humanenergy metabolism provides several advantages. The advantages of theapparatus include, but are not limited to:

-   -   1. Measuring and correcting for stray capacitances.    -   2. Minimizing input noise and reduces capacitances of connecting        cables.    -   3. Measuring and eliminating offset voltage at six measuring        points and reduces noise by    -   hardware and software means at six measuring points.    -   4. Providing high output resistance and low output reactance of        the current sources.    -   5. Minimizing noise due to analog-digital conversion.    -   6. Providing information on performance and reliability of        measurements.    -   7. Providing individualized measurements of the extracellular        and intracellular water mass and fat and lean body mass.

The advantages of dynamic indirect individualized measurement include,but are not limited to:

-   -   1. Providing individualized self-correcting and self-adaptive        modeling of the human energy metabolism.    -   2. Providing real-time calculation of components of the human        energy metabolism.    -   3. Allowing for inverse calculations and for inferring unknown        input data from output results.    -   4. Allowing for real-time calculations in a freely moving human        subject with the need for measurements only in 24 hour        increments.    -   5. Allowing for dynamic serial measurements of the body        composition change where the metabolic model is fitted to the        measured data and by using error measurements of the model which        becomes individualized and self-adaptive.    -   6. Allowing for calculating the macronutrient oxidation rates.    -   7. Allowing for estimation of the utilized macronutrient intake.    -   8. Allowing for detecting the unknown part of the energy        metabolism and the error of metabolic model estimations.    -   9. Allowing for identification of parameters of lipid        degradation and gluconeogenesis from protein.    -   10. Allowing for intra- as well as inter-individual comparisons        of the indirectly measured metabolic parameters when using the        canonical representation of the human energy metabolism, which        allows quantitative characterization of the metabolism and        enhances understanding of individual variations and predicts the        effect of dietary and exercise interventions.    -   11. Allowing for trend or trajectory calculations of the lean        body mass and fat mass to predict future changes quantitatively        based on the daily energy density of the lean body mass change        and the daily energy density of the fat mass change        calculations.    -   12. Displaying a strong correlation between the R-ratio and        other surrogate markers of insulin resistance such as the        HOMA-IR (homeostasis assessment model of insulin resistance) and        it can serve as a surrogate measure for non-invasive tracking of        the insulin resistance change.    -   13. Using the R-ratio to estimate fat oxidation and gage        indirectly mitochondrial dysfunction.

While the above description contains many specificities, these are notlimitations on the scope, but rather as an illustration of an exampleembodiment. For example, the apparatus can:

-   -   1. Have a multiplicity of measuring circuits to allow segmental        measurements of the parts of the human body.    -   2. Take measurements continuously rather than just daily or        intermittently.    -   3. Accommodate complex lumped network models of the human body        consisting of a multitude of resistances, capacitances, and        inductances.    -   4. Obtain measurements at a higher frequency than 1 megahertz.    -   5. Measure the capacitances of the excitation electrodes and        sensory electrodes.    -   6. Measure frequency dependent characteristics of the human        tissue.

Further, the dynamic indirect individualized measurement method can, forexample, be extended to measure dynamically:

-   -   1. The de novo lipogenesis.    -   2. The glycerol 3-phosphate synthesis.    -   3. The gluconeogenesis from glycerol.    -   4. The synthesis or burning of visceral fat and other segmental        fat masses of a body segment.    -   5. The building or wasting of segmental muscle masses of a body        segment.    -   6. The total energy expenditure.    -   7. The physical activity energy expenditure.    -   8. A daily change of lean body mass, a daily change of body fat        mass, a daily change of protein mass; a daily utilized        carbohydrate intake; a daily utilized fat intake; a daily        utilized protein intake; a daily rate of carbohydrate oxidation;        a daily rate of fat oxidation; a daily rate of protein        oxidation; a daily parameter for energy flux from carbohydrate        pool to fat pool; a daily parameter for uncounted energy; a        daily energy density of the lean body mass change; a daily        energy density of the fat mass change; and a daily R-ratio for        tracking changes of insulin resistance using the R-ratio method        using a Canonical Model Form of the Human Energy Metabolism        method operating on portable computers or smart phones.

FIG. 6 and FIG. 7A to 7I of present disclosure on systems and methodsfor high frequency impedance spectroscopy detection of daily changes ofdielectric properties of the human body to measure body composition andhydration status are now described in detail.

FIG. 6 and FIG. 7A to 7I show an alternative embodiment of the apparatusand method for the analysis of body composition and hydration status 109as in FIGS. 1A and 1B. The high frequency four electrode excitationapparatus for the analysis of the human body's foot-to-foot electricalimpedance and the errors of measurements as shown in FIG. 6 and FIG. 7Ato 7I are primarily designed to work in the high frequency range,typically 100,000 kHz to 10 MHz. This is the frequency range which hascaused many difficulties in conventional bioelectric impedancemeasurement mainly because the stray capacitances are not negligible.⁴⁷The challenging issue is to measure the human body's resistance at anextrapolated infinite frequency. Finding the human body's resistance atan estimated zero frequency poses far less technical challenge. ⁴⁷Scharfetter et al, DOI:10.1088/0967-3334/19/2/012

The high frequency four electrode excitation apparatus for the analysisof the human body's foot-to-foot electrical impedance and the errors ofmeasurements as in FIG. 6 and FIG. 7A to 7I work as a process divided upin three parts:

-   -   1. The first part is the impedance measurement of the human        body. Impedance values of the human body are measured at        pre-programmed frequencies. Error analysis of the primary data        collection is used to recognize and reject flawed results.    -   2. The second part is fitting a parametric model of human        impedance. The traditional Cole model is used to fit to the        measured impedance values. Model parameters are determined.        These are the resistance at an estimated zero frequency, the        resistance at an extrapolated infinite frequency, the        characteristic time of relaxation, and the alpha exponential        symbol of relaxation time dispersion. Error checking of the        curve fitting procedure is performed. In case of modeling error,        the data will be fitted to an extended version of the Cole model        or to an individual impedance model introducing more parameters        than in the original Cole model.    -   3. The third part is predicting the hydration status and body        composition changes. A statistical calculation is performed here        to predict the most likely change of hydration status and body        composition since the last measurement is compared to the        reference method.

The high frequency four electrode excitation apparatus for the analysisof the human body's foot-to-foot electrical impedance and the analysiserrors is a second embodiment of the first embodiment of the measuringdevice for hydration status and body composition changes represented inFIG. 1A, 109 of the U.S. patent application Ser. No. 14/541,033“Apparatus And Method For The Analysis Of The Change Of Body CompositionAnd Hydration Status And For Dynamic Indirect IndividualizedMeasurements Of The Human Energy Metabolism” and in FIG. 2 to FIG. 5V.One important innovation is that the unidirectional flow of measurementdata from the apparatus to the method becomes bidirectional because themethod also supplies data to the apparatus. In this application, the apriori knowledge of predictable and expected change of the human bodycomposition and hydration status calculated by the method improves theaccuracy, validity, consistency, reliability, stability, and robustnessof the measured results of the daily change of the extracellular watermass, intracellular water mass, lean body mass, fat mass, and proteinmass.

Part One: Impedance Measurement of the Human Body

The goal of this measurement is to determine the unknown compleximpedance Z_(i)* of the human body to a current flow I_(i)* through themeasured segments of the body at the predetermined frequencies f_(i),702. The measurements are fitted to an electric circuit model whichdescribes the resistive and capacitive properties of the human bodylocated between the sensing electrodes C1 and C2 of FIG. 6. Themeasurement procedure determines the complex impedance Z_(i)* andcurrent flow I_(i)* as well as measurement and modeling errors. The modeof operation is cyclic and it is performed at preset frequencies f_(i)ranging from 100 kHz up to 10 MHz.

The first realization of the high frequency four-electrode-excitationmethod is described here. A standup scale combined with the necessaryelectronics will perform the procedure. A user will stand on the scalewith both feet positioned properly on the scale in the marked areas. Thedistal excitation electrode A1 for the right foot and A2 for the leftfoot will be snugly placed into the skin fold between the proximal toeend and distal forefoot of FIG. 6. The distal excitation electrodes B1for the right foot and B2 for the left foot in FIG. 6 will nestle at thehighest elevation and medial portion of the plantar arch. The sensingelectrodes C1 for the right foot and C2 for the left foot in FIG. 6 aresituated in front of the heel area which is pressing down on the scale.

The microcontroller unit organizes the process of parallel excitation onthe excitation electrodes A1, A2, B1, B2 with simultaneous measurementsat the sensing electrodes C1, C2 of FIG. 6. Voltmeters VAT1, VRA 1,VBT1, VRB 1, V1 in FIG. 6 measure the amplitude, phase and offset of thesignals for the right foot and voltmeters VAT2, VRA 2, VBT2, VRB 2, V2of FIG. 6 measure the amplitude, phase and offset of the signals for theleft foot. For finding the amplitude, phase and offset of a captured anddigitalized voltage signal, it may be preferable to use the IEEE Std.1057, “An Algorithm for Three Parameter (Known Frequency) Least SquaredFit to Sine-Wave Data”.⁴⁸ This method provides the root mean squareerror, which was calculated from the best-fit sine wave. The root meansquare error is used as the primary screening for errors in the primarydata. ⁴⁸ IEEE Trial-Use Standard for Digitizing Waveform Records, pg.13-14.

The high frequency four electrode excitation apparatus for the analysisof the human body's foot-to-foot electrical impedance and measurementserrors represent an improved and second embodiment of the firstembodiment of the apparatus for body composition and hydration statusmeasurement as shown in process 109 of FIG. 1A containing processes 106,107 and 108 of FIG. 1A, as described in the utility patent applicationSer. No. 14/541,033 filed on Nov. 13, 2014 and the provisional patentapplication Ser. No. 62/372,363, filed on Aug. 9, 2016. The measurementprocess starts at 701 of FIG. 7A and ends with reaching the connectors Vand W of FIG. 1A.

Part one, Stage 1, 703.

Voltage sources UAT1, UAT2, UBT1 and UBT2 of FIG. 6 are turned on at thedesired measuring frequency f_(i). Voltage source switches SA1, SB1, SA2and SB2 of FIG. 6 are also turned on. The absolute value of theamplitude voltage sources UAT1 is approximately 1 Volt at the excitationelectrode AT1 of FIG. 6 and this value is used as a reference point forall other voltage sources, i.e. for UAT2, UBT1, and UBT2. The absolutevalue of the amplitude of the voltage sources UAT2, UBT1 and UBT2 arechosen in a way that the voltage values at measuring electrodes C1 andC2 of FIG. 6 become equal and are as close as possible to zero. Toobtain a balanced resistance bridge, the voltage source UAT1 is used asthe reference source for the phase value so that the phase of voltagesource UAT2 will have the same phase as UAT1. The phase values ofvoltage sources of UBT1 and UBT2 will be close to the opposite phase ofUAT1, while adjusting the phase of UBT1 and UBT2 to satisfy the requiredcondition that the voltage values at the sensing electrodes at C1 and C2of FIG. 6 measured with voltmeters V1 and V2 of FIG. 6 have near zeropositive value for both the real and imaginary part of the measuredvoltage. This tuning maneuver can be made faster by using the voltagesource switches SA1, SB1, SA2 of FIG. 6 and SB2 of FIG. 6. In this case,the UBT1 voltage source is adjusted so that the voltage at V2 attains anear zero positive value for both the real and imaginary part of themeasured voltage while switches SA2 and SB2 are in the off position.Then UBT2 voltage source is adjusted so that the voltage at V1 attains anear zero positive value for both real and imaginary part of themeasured voltage while switches SA1 and SB1 are in the off position.

To obtain the unknown admittance values Y_(AAB 1), Y_(B 1), Y_(BCC 1),Y_(C) 1, Y_(AAB 2), Y_(B 2), Y_(BCC 2), and, Y_(C 2) of FIG. 6,Kirchhoff s first and second law for circuit analysis are used.

Directly measured current flow values are: I^(S1) _(A1) at VRA 1 acrossresistance RA 1 of FIG. 6, I^(S1) _(B1) at VRB 1 across resistance RB 1of FIG. 6, I^(S1) _(A2) at VRA 2 across resistance RA 2 of FIG. 6, andI^(S1) _(B2) at VRB 2 across resistance RB 2 of FIG. 6. Directlymeasured voltage values are U^(S1) _(A1) by adding up the voltages atVRA 1+VAT1, U^(S1) _(B1) by adding up the voltages at VRB 1+VBT1, U^(S1)_(A2) by adding up the voltages at VRA 2+VAT2, and U^(S1) _(B2) byadding up the voltages at VRB 2+VBT2.

The current flow through electrode C1 I^(S1) _(IN1)* is indirectlymeasured and it is calculated from the known value of Y_(IN1)*characteristic to the sensing instrument V1 and the directly measuredU^(S1) _(C1) with V1 as in Eq. 301. The current flow through electrodeC2 I¹ _(IN2)* is indirectly measured and it is calculated from knownvalue of Y_(IN2)* characteristic to the sensing instrument V2 and thedirectly measured U^(S2) _(C2) with V2 as in Eq. 302. Thesecharacteristics are known admittance values and are obtained from thesensing device's manufacturer. An expected current loss I^(S1) _(loss1)*appears which is not flowing through the measured portion of the body orthrough sensing electrode C1. The value of I^(S1) _(loss1)* iscalculated with Eq. 303. Likewise, an expected current loss I^(S1)_(loss2)* appears which is not flowing through the measured portion ofthe body or through sensing electrode C2. The value of I^(S1) _(loss2)*is calculated with Eq. 304. The current losses I^(S1) _(loss1)* andI^(S1) _(loss2)* represent error of measurement. This will appearbecause of stray capacitances on both feet and the current leakage toground and to earth potential. This current loss is modeled byadmittance Y_(Loss 1) for the right foot and admittance Y_(Loss 2) forthe left foot; their values are calculated in Eq. 305 and Eq. 306,respectively.

For the first realization of the high frequencyfour-electrode-excitation method the following assumptions are made:

-   -   1. The following equations are valid for admittances        Y_(B 1)=Y_(C 1), Y_(B 2)=Y_(C 2), Y_(AAB 1)=Y_(BCC 1), and        Y_(AAB 2)=Y_(BBC 2) where Y_(B 1) represents the reciprocal        value of the resistance ZB 1 of FIG. 6, Y_(C 1) represents the        reciprocal value of the resistance ZC 1 of FIG. 6, Y_(B 2)        represents the reciprocal value of the resistance ZB 2 of FIG.        6, Y_(C 2) represents the reciprocal value of the resistance ZC        2 of FIG. 6, Y_(AAB 1) represents the reciprocal value of the        resistance of ZA 1+ZAB1 of FIG. 6, Y_(BCC 1) represents the        reciprocal value of the resistance ZBC 1+ZC 1 of FIG. 6,        Y_(AAB 2) represents the reciprocal value of the resistance of        ZA 2+ZAB2 of FIG. 6, and Y_(BCC 2) represents the reciprocal        value of the resistance ZBC 2+ZC 2 of FIG. 6.    -   2. Further, it is assumed that a successful tuning of the        amplitude and phase of voltage sources of UBT1 and UBT2 are        possible to achieve U^(S1) _(C1)≈U^(S1) _(C2) with values as        closest as possible to zero and that this process will result in        a voltage V^(S1) _(C1)* between resistances ZBC 1 of FIG. 6 and        ZC 1, as well as in a voltage value V^(S1) _(C1)* between        resistances ZBC 2 of FIG. 6 and ZC 2 to be quasi equal i.e.        V^(S1) _(C1)*≈V^(S1) _(C2)* and with closest possible values to        zero. Essentially, we are trying to make the voltages at these        nodes to be approximately equal to each other and as close as        possible to zero. At the same time, the magnitude of the current        losses I^(S1) _(loss1)* and I^(S1) _(loss1)* approaches minimal        value approximating zero.

The value of Y_(B 1) is calculated with Eq. 307. The value of Y_(B 2) iscalculated with Eq. 308. The voltage V^(S1) _(B1)* at junction point ZAB1 of FIG. 6 with ZBC 1 and ZB 1, and the voltage value V^(S1) _(B2)* atjunction point ZAB 2 of FIG. 6 with ZBC 2 and ZB 2 are calculatedindirectly with Eq. 309 and Eq. 310 respectively. The value of Y_(C 1)is calculated with Eq. 311. The value of Y_(C 2) is calculated with Eq.312. The value of Y_(BCC 1) is calculated with Eq. 313. The value ofY_(BCC 2) is calculated with Eq. 314. The value of Y_(AAB 1) iscalculated with Eq. 315. The value of Y_(ABB 2) is calculated with Eq.316. The voltage value V^(S1) _(C1)* at junction point ZBC 1 with ZC 1,and the voltage value V^(S1) _(C2)* at junction point ZBC 2 with ZC 2are calculated indirectly with Eq. 317 and Eq. 318, respectively.

The next step is to calculate the impedance values of ZA 1, ZAB 1, ZB 1,ZBC 1, ZC 1, ZA 2, ZAB 2, ZB 2, ZBC 2, and ZC 2 in FIG. 6. Thereciprocal value of Y_(AAB 1) will give ZA 1+ZAB 1; taking thereciprocal value of Y_(B 1) will give ZB 1; taking the reciprocal valueof Y_(BCC 1) will give ZB 1+ZBC 1; taking the reciprocal value ofY_(C 1) will give ZC 1; taking the reciprocal value of Y_(AAB 2) willgive ZA 2+ZAB 2; taking the reciprocal value of Y_(B 2) will give ZB 2;taking the reciprocal value of Y_(BCC 2) will give ZB 2+ZBC 2; andtaking the reciprocal value of Y_(C 2) will give ZC 2.

Part one, Stage 2, 706.

Voltage sources UAT1, UBT1, UAT2, UBT2 are turned on at the desiredmeasuring frequency f_(i). Voltage source switches SA1, SB1, SA2 and SB2are also turned on. The absolute value of the amplitude voltage sourcesUAT1 is approximately 1 Volt at the excitation electrode AT1 and thisvalue is used as a reference point for all the other voltage sources,i.e. for UAT2, UBT1, and UBT2. The absolute value of the amplitude ofthe voltage sources UAT2, UBT1 and UBT2 remain the same as in stage 1.Using the voltage source UAT1 as the reference source for the phasevalue, the phase of the voltage source UAT2 will have the same phase asthe UAT1 phase. The phase values of voltage sources of UBT1 and UBT2will be close to the same phase as the reference voltage source UAT1.

For the first realization of the high frequencyfour-electrode-excitation method, it is assumed that a successful tuningof the amplitude and phase of the voltage sources UBT1 and UBT2 arepossible to achieve U^(S2) _(C1)≈U^(S2) _(C2) and that this process willresult in a voltage U^(S1) _(C1)≈U^(S1) _(C2) between the resistancesZBC 1 and ZC 1, as well as in a voltage value V^(S2) _(C2)* between theresistances ZBC 2 and ZC 2 which have the same amplitude and phase, i.e.V^(S2) _(C1)*≈V^(S1) _(C2)*.

It is assumed here that under these conditions there will be ameasurable current flow I^(S2) _(Cb1) which is channeled through thehuman body stray capacitance C_(b1) to ground in FIG. 6 and that thereis also a measurable current flow I^(S2) _(Cb2) which is channeledthrough the human body stray capacitance C_(b2) of FIG. 6. It is furtherassumed that there will be a current flow I^(S2) _(loss1)* at the rightfoot and a current flow I^(S2) _(loss2)* at the left foot bypassing themeasured segment of the human body between the sensing electrodes C1 andC2.

Directly measured current flow values are: I^(S2) _(A1) at VRA 1 acrossresistance RA 1 of FIG. 6, I^(S2) _(B1) at VRB 1 across resistance RB 1of FIG. 6, I^(S2) _(A2) at VRA 2 across resistance RA 2 of FIG. 6, andI^(S2) _(B2) at VRB 2 across resistance RB 2 of FIG. 6. Additionaldirectly measured values are: U^(S2) _(A1) by adding up the voltages atVRA 1+VAT 1, I^(S2) _(B1) at VRB 1+VBT1, I^(S2) _(A2) at VRA 2+VAT 2,and I^(S2) _(B2) at VRB 2+VBT2.

The current flowing through electrode C1 I^(S2) _(IN1)* is indirectlymeasured and it is calculated from the known value of the Y_(IN1)*characteristic to the sensing instrument V1 and the directly measuredU^(S2) _(C1) with V1 as in Eq. 319. The current flowing throughelectrode C2 I_(IN2) ¹* is indirectly measured and it is calculated fromthe known value of the Y_(IN2)* characteristic to the sensing instrumentV2 and the directly measured U^(S2) _(C2) with V2 as in Eq. 320. Thesecharacteristics are known admittance values and are obtained from thesensing device's manufacturer. Indirectly measured U^(S2) _(C1)* iscalculated as in Eq. 321. Similarly, indirectly measured U^(S2) _(C2)*is calculated as in Eq. 322.

An expected current loss I^(S2) _(loss1)* at the right foot appearswhich is not flowing through the measured portion of the body northrough the sensing electrode C1. The value of I^(S2) _(loss1)* iscalculated with Eq. 323. Likewise, an expected current loss I^(S2)_(loss1)* at the left foot appears which is not flowing through themeasured portion of the body or through the sensing electrode C2. Thevalue of I^(S2) _(loss1)* is calculated with Eq. 324.

The indirectly measured current flow I^(S2) _(Cb1)* which is channeledthrough the human body stray capacitance C_(b1) and the current flowI^(S2) _(Cb2)* which is channeled through the human body straycapacitance C_(b2) are calculated as in Eq. 325 and Eq. 326respectively. The susceptance values Y_(Cb1) and Y_(Cb2) of the humanbody stray capacitance C_(b1) and C_(b2) are calculated as in Eq. 327and Eq. 328 respectively.

Part one, Stage 3, 707:

Voltage sources UAT1, UBT1, UAT2, UBT2 are turned on at the desiredmeasuring frequency f_(i). Voltage source switches SA1, SB1, SA2 and SB2are also turned on. The absolute value of the amplitude voltage sourcesUAT1 is approximately 1 Volt at the excitation electrode AT1 and thisvalue is used as a reference point for all the other voltage sources,i.e. for UAT2, UBT1, and UBT2. The absolute value of the amplitude ofthe voltage sources UAT2, UBT1 and UBT2 remain the same as in stage 2.Using the voltage source UAT1 as the reference source for the phasevalue the phase of voltage source UBT1 will be in the same phase as UAT1and UAT2 and UBT2 will have the opposite phase as UAT1.

For the first realization of the high frequencyfour-electrode-excitation method, it is assumed that a successful tuningof amplitude and phase of voltage sources UBT1 and UBT2 are possible toachieve U^(S3) _(C1)≈−U^(S3) _(C2) and this process will result in avoltage V^(S3) _(C1)* between resistances ZBC 1 and ZC 1, as well as ina voltage value V^(S3) _(C2)* between resistances ZBC 2 and ZC 2 whichhave the same amplitude but opposing phase, i.e. V^(S2) _(C1)*≈−V^(S2)_(C2)*.

It is assumed here that under these conditions there will be ameasurable current flow I^(S3) _(Cb1) which is channeled through thehuman body stray capacitance C_(b2) to ground and that there is also ameasurable current flow I^(S3) _(Cb2) which is channeled through thehuman body stray capacitance C_(b2). Further, it is assumed that therewill be a current flow I^(S3) _(loss1)* at the right foot and a currentflow I^(S3) _(loss2)* at the left foot bypassing the measured segment ofthe human body between sensing electrodes C1 and C2.

Directly measured current flow values are: I^(S3) _(A1) at VRA 1, I^(S3)_(B1) at VRB 1, I^(S3) _(A2) at VRA 2, and I^(S3) _(B2) at VRB 2.Additional directly measured values are: U^(S3) _(A1) by adding up thevoltages at VRA 1+VAT1, U^(S3) _(B1) at VRB 1+VBT1, U^(S3) _(A2) at VRA2+VAT2, and U^(S3) _(B2) at VRB 2+VBT2.

The current flow through electrode C1 I^(S3) _(IN1)* is indirectlymeasured and it is calculated from known value of Y_(IN1)*characteristic to the sensing instrument V1 and the directly measuredU^(S3) _(C1) with V1 as in Eq. 329. The current flow through electrodeC2 I^(S3) _(IN2)* is indirectly measured and it is calculated from knownvalue of Y_(IN2)* characteristic to the sensing instrument V2 and thedirectly measured U^(S3) _(C2) with V2 as in Eq. 330. Thesecharacteristics are known admittance values and are obtained from thesensing device's manufacturer. Indirectly measured V^(S3) _(C1)* iscalculated as in Eq. 331. Similarly, indirectly measured V^(S3) _(C2)*is calculated as in Eq. 332.

An expected current loss I^(S3) _(loss1)* at the right foot appears atthe node between ZBC 1 and ZC 1 wherein the current flows directly tothe ground and away from electrodes A1, B1, and C1. This current alsoflows away from the measured portion of the body, which occurs betweenthe nodes ZBC 1 and ZC 1 of the right foot and nodes ZBC 2 and ZC 2 ofthe left foot. The value I^(S3) _(loss1)* is calculated with Eq. 333.Likewise, an expected current loss I^(S3) _(loss2)* at the left footalso appears at the node between ZBC 2 and ZC 2 wherein the currentflows directly to the ground and away from electrodes A2, B2, and C2.This current also flows away from the measured portion of the body,which occurs between the nodes ZBC 2 and ZC 2 of the left foot and nodesZBC 1 and ZC 1 of the right foot. The value of I^(S3) _(loss2)* iscalculated with Eq. 334. (NOTE: ZC 1 and ZBC 1 denote the right foot,and ZC2 and ZBC 2 denote the left foot).

The indirectly measured current flow I^(S3) _(Cb1)* which is channeledthrough the human body stray capacitance C_(b1) and the current flowI^(S3) _(Cb2)* which is channeled through the human body straycapacitance C_(b2) are calculated as in Eq. 335 and Eq. 336,respectively.

The current flowing through the measured part of body between C1 and C2is I_(i)* and it is calculated as in Eq. 337. The unknown impedancebetween measurement electrodes C1 and C2 is Z_(i)* at frequency f_(i)and it is calculated as in Eq. 338.

Part Two: Fitting a Parametric Model of Human Impedance

The primary goal of this measurement is to determine the unknownresistance at an estimated zero frequency R₀ and resistance at anextrapolated infinite frequency R_(∞) with the help of a parametricmodel of the human impedance. The secondary goal is to arrive at anindividual impedance model that is in strong agreement with thesubject's impedance values during serial measurements. These goals areachieved in two stages. In stage one, the measured impedance values arefitted to the traditional Cole model. In stage two, the result of thefitting procedure is examined for statistical validity. If thetraditional Cole model does not explain well the measured impedancevalues, then the traditional Cole model will be discarded and replacedby an extended version of the traditional Cole model which introducesmore model parameters. At the end of part two, the unknown resistance atan estimated zero frequency R₀ and the resistance at an extrapolatedinfinite frequency R_(∞) are calculated from the accepted model of thehuman impedance.

Part two, Stage 1, 708.

The weight factors w_(i) are calculated as in Eq. 339 which is thereciprocal value of the variance σ_(i) ² of the measured impedancevalues Z_(i)* at frequency f_(i) by repeating these measurementsmultiple times. The Unconstrained Nonlinear Least Square Programingprocedure will determine the following parameters:

-   -   1. Resistance at an estimated zero frequency R₀, resistance at        an extrapolated infinite frequency R_(∞).    -   2. Time constant T.    -   3. Exponent symbol α of the equivalent mathematical circuit        model at frequency f_(i) of the traditional Cole model as in Eq.        340 by using the measured impedance values Z_(i)* and minimizing        the sum of error squares S as calculated in Eq. 341.

S becomes how well the parameter displays characteristics of χ²distribution. Examining S with the so called χ² test can result inrejection or acceptance of the traditional Cole model, 709. If thetraditional Cole model in Eq. 340 is accepted as a good fit to the data,Z_(i)*, then stage 1 ends here and the model parameter resistance at anestimated zero frequency R₀ and the resistance at an extrapolatedinfinite frequency R_(∞) are accepted for further calculations in PartThree. If this is not the case, then the process will proceed with parttwo, stage 2.

Part two, Stage 2, 710.

An extended version of the Cole model is considered which could take themathematical form as in Eq. 342. The Unconstrained Nonlinear LeastSquare Programing procedure will determine the following parameters:resistance at an estimated zero frequency R₀, resistance at anextrapolated infinite frequency R_(∞), characteristic time constant τ,alpha exponential symbol of relaxation time dispersion α, and the betaexponential symbol of relaxation time dispersion β as in Eq. 342 byusing the measured impedance values Z_(i)* and minimizing the sum oferror squares SE as calculated in Eq. 342, 710. SE becomes how well thefit parameter displays characteristics of χ² distribution. Examining SEwith the χ² test can result in rejection or acceptance of the extendedCole model, 711. If the extended Cole model in Eq. 340 is accepted as agood fit to the data, Z_(i)*, then part two ends here and the modelparameter resistance at an estimated zero frequency R₀ and theresistance at an extrapolated infinite frequency R_(∞) are accepted forfurther calculations as in part three. If this is not the case, then theprocess will proceed to look for an individualized model Z_(i) ^(M) (R₀,R_(∞), τ₁, . . . τ_(M), α, β) introduces another parameter: thefirst-time constant of relaxation τ₁ up to Mth time constant ofrelaxation τ_(M) where M is chosen to be a low integer. The process offinding the appropriate individualized model ends as soon as the SMcalculated by Eq. 344 shows a good fit and using the χ² test can resultin acceptance of the individualized model Z_(i) ^(M) (R₀, R_(∞), τ₁, . .. τ_(M), α, β) 712.

Part Three: Prediction of Hydration Status and Body Composition Changes

The primary goal here is to predict the hydration status i.e.extracellular water mass ECW′_(k) and intracellular water mass ICW′_(k)as well as body composition consisting of lean body mass L′_(k)m fatmass F′_(k), and protein mass P′_(k) for the day of measurement k. Thesegoals are achieved in three stages. In the first stage, the ratio of theextracellular water ECW_(k)* to total body water mass TBW_(k)* for theday k is calculated, then the quasi stable extracellular water mass tototal water mass is estimated. In the second stage, a constrained modelfitting of the impedance values Z_(i)* to the chosen impedance model isused to derive the extracellular water mass ECW_(k)* and total watermass TBW_(k)* for the day k. In the third stage, a constrained modelfitting of the impedance values Z_(i)* to the chosen impedance model isused to arrive at lean body mass L′_(k), fat mass F′_(k), and proteinmass P′K, for the day of measurement k.

Part three, Stage 1, 713.

The results, i.e. the resistance at an estimated zero frequency R₀ andresistance at an extrapolated infinite frequency R_(∞), of theunrestrained curve fitting of part two, are used to calculate the ratioRET_(k)* of the extracellular water ECW_(k)* to total body water massTBW_(k)* for the day k as in Eq. 345. The reference value of theadjustable coefficient to calculate extracellular water mass kECW_(j)*on day j and the reference value of the adjustable coefficient tocalculate intracellular water kICW_(j)* on day j is obtained fromprocess equations Eq. 144 and Eq. 145 of the apparatus and method forthe analysis of the change of body composition and hydration status andfor dynamic indirect individualized measurements of the human energymetabolism as in FIG. 1 to FIG. 5V. The statistical estimation of thevalue of the quasi stationary ratio

_(k) of the extracellular water to total body water is performed withthe Kalman filter as in Eq. 346 where the Kalman gain KRET_(k) iscalculated as a scalar process.⁴⁹

_(k−1) represents the estimated ratio on the previous day. ⁴⁹ Grewal etal, “Kalman filtering theory and practice using MATLAB”. Third Edition,John Wiley & Sons, New Jersey, 2008.

Part three, Stage 2, 713.

A Nonlinear Least Square Programing procedure using Lagrange multiplieris used for constrained model fitting to the chosen individualizedimpedance model Z_(i) ^(M) to the impedance values Z_(i)* in order toderive the extracellular water mass ECW′_(k) and intracellular watermass ICW′_(k) for the day k. The sum of error squares of the constrainedindividualized model fitting for hydration status is represented in Eq.347. The weight factors w_(i) are calculated as in Eq. 339, which arethe reciprocal value of the variance a of the measured impedance valuesZ_(i)* at frequency f_(i) by repeated measurements. λ₁ represents theLagrange multiplier. h₁ is the equation Eq. 348 for the constraint setby the quasi stationary ratio

_(k) of the extracellular water mass to total body water mass on day k.The result of the constrained Nonlinear Least Square Programingprocedure using Lagrange multiplier provides the resistance of the humanbody at an estimated zero frequency R₀ ^(HS)′ and an extrapolatedinfinite frequency R_(∞) ^(HS)′ satisfying the constraint in h₁. Theextracellular water mass ECW_(k) ^(HS)′ and intracellular water massICW_(k) ^(HS)′ are determined by Eq. 349 and Eq. 350, respectively. Hrepresents body height in cm and W_(k) the body weight in kg on day k.

Part three, Stage 3, 714, 715, 716.

First Embodiment of Part Three Stage Three

The first embodiment of part three, stage 3 is the combined use of thehigh frequency four electrode excitation apparatus for the analysis ofthe human body's foot-to-foot electrical impedance and the analysiserrors as shown in FIG. 7A-7I and the method for the analysis of thechange of body composition and hydration status and for dynamic indirectindividualized measurements of the human energy metabolism as shown inFIG. 5A with bidirectional data flow. The error of estimation can beminimized with the a priori knowledge of the previous changes of theglycogen store ΔG_(k), and the previous changes of the protein massΔP_(k). The previous changes of the glycogen store change ΔG_(k) can beobtained by Eq. 111, replacing the less accurate calculation of Eq. 359.The previous changes of the protein store change ΔP_(k) can be obtainedby Eq. 113, replacing the less accurate calculation of Eq. 358.

Second Embodiment Of Part Three Stage Three

An alternative embodiment of part three, stage 3 is the standalone useof the high frequency four electrode excitation apparatus for theanalysis of the human body's foot-to-foot electrical impedance and theanalysis errors as shown in FIG. 6 and FIG. 7A to 7I without using theapparatus and method for the analysis of the change of body compositionand hydration status and for dynamic indirect individualizedmeasurements of the human energy metabolism as shown in FIG. 1 to FIG.5V.

A Nonlinear Least Square Programing procedure using Lagrange multiplieris used for constrained model fitting of the chosen individualizedimpedance model Z_(i) ^(M) to the impedance values Z_(i)* to derive thelean body mass L′_(k), the fat mass F′_(k), and the protein mass P′_(k)for the day of measurement k. The sum of error squares of theconstrained individualized model fitting for body composition isrepresented in Eq. 351. The weight factors w_(i) are calculated as inEq. 339 which is the reciprocal value of the variance σ_(i) ² of themeasured impedance values Z_(i)* at frequency f_(i) by repeatedmeasurements. λ₂ represents the Lagrange multiplier. h₂ is the equationEq. 369 with constraints set forth by five fixed ratios betweendifferent compartments of the human body. The fixed ratio of lean bodymass to total body water⁵⁰ is in Eq. 352. The fixed ratio of lean cellmass to intracellular water⁵¹ is in Eq. 353. The fixed ratio of proteinmass to lean cell mass is in Eq. 354. ⁵⁰ Jaffrin et al, DOI:10.1016/j.medengphy.2008.06.009⁵¹ Hall, DOI:10.1152/ajpendo.00559.2009

The fixed ratio of total body mass to bone mass is in Eq. 355. The fixedratio of extracellular protein mass minus fraction of bone mass toextracellular mass is in Eq. 356. The body composition changes sincelast calibration day j for lean mass ΔL_(k) are calculated as in Eq.357; for protein mass ΔP_(k) are calculated as in Eq. 358; and forglycogen mass ΔG_(k) are calculated as in Eq. 359. The size of theglycogen mass G_(k) is calculated in Eq. 360. The mass of intracellularsolutes ICS is calculated with Eq. 361. The size of bone mass BM iscalculated with Eq. 362. The size of extracellular protein mass ECP_(k)is calculated with Eq. 363. The size of protein mass P_(k) is calculatedwith Eq. 364. The constraint h₂ in equation Eq. 369 is built from thetwo equations Eq. 365 and Eq. 366. Specifically, Eq. 366 is subtractedfrom Eq. 365, wherein the result is equal to zero, as shown in Eq. 367.This constrains h₂ because the result of the subtracting the twoequations must be zero as shown in Eq. 367. Eq. 365 shows thecompartmentalized lean body mass calculation, while Eq. 366 shows thecalculation from the extracellular water mass ECW_(k)* and intracellularwater mass ICW_(k)*.

The equation Eq. 368 shows the substitutions for protein mass P_(k),glycogen mass G_(k), intracellular solute ICS, extracellular proteinmass ECP_(k) and bone mass BM with the expressions showing thedependency from either the extracellular water mass ECW_(k)* or theintracellular ICW_(k)* water mass. In equation Eq. 369, theextracellular water mass ECW_(k)* or the intracellular ICW_(k)* watermass is replaced with Eq. 148 and Eq. 149 from the “apparatus and methodfor the analysis of the change of body composition and hydration statusand for dynamic indirect individualized measurements of the human energymetabolism” as shown in FIG. 1 to FIG. 5V. The result of the constrainedNonlinear Least Square Programing procedure using Lagrange multiplierprovides the resistance of the human body at an estimated zero frequencyR₀ ^(BC)′ and an extrapolated infinite frequency R_(∞) ^(BC)′ satisfyingthe constraint in h₂.

The extracellular water mass ECW_(k) ^(BC)′ and intracellular water massICW_(k) ^(BC)′ are determined by Eq. 370 and Eq. 371, respectively. Hrepresents body height in cm and W_(k) the body weight in kg on day k.The lean body mass L′_(k) is calculated by Eq. 372, the fat mass F′_(k)is calculated by Eq. 373, and the protein mass P′_(k) is calculated byEq. 374 for the day of measurement k.

Thus, it can be seen that at least one embodiment of the high frequencyfour electrode excitation apparatus for the analyses of the human body'sfoot-to-foot electrical impedance and the errors of measurements providefor a measurement and individualized modeling of the human body'selectrical impedance, as well as a prediction of extracellular andintracellular water compartments changes and body composition changes.

The advantages of the present disclosure's “systems and methods for highfrequency impedance spectroscopy detection of daily changes ofdielectric properties of the human body to measure body composition andhydration status” over prior art include, but are not limited to:

-   -   1. Measuring the impedance of 4 excitation electrodes and 2        measuring electrodes without using input logic circuits.    -   2. Measuring simultaneously the body weight and complex        electrical impedance of the human body at a multitude of        frequencies ranging from 100 kHz to 10 MHz in standing positions        between two sensing electrodes. The arrangement of the        electrodes is such that they are in contact with the thinnest        skin areas of the foot. Specifically, the electrodes have the        best contacts through the thinnest skin areas of the foot with        an arrangement forcing the user to maintain the same electrode        position during repeated measurements.    -   3. Measuring stray capacitance of the measured body segment        between the two sensing electrodes and separately the stray        capacitances outside of the measured body segment which include        the stray capacitances of both feet and the measuring        instrumentation itself.    -   4. Registering environmental factors at the time of measurement        including location, room temperature, local environmental        electromagnetic influences and notes physiological factors such        as accurate body weight, time of the measurement, duration of        measurement, and skin temperature.    -   5. Measuring common ground potential and compensates for        asymmetric arrangements of the measuring objects and varying        electrode impedances.    -   6. Measuring electrical voltage signals at 10 measuring points,        digitizing the signal, fitting it with sine wave function, and        determining amplitude, phase, offset and the sum of the least        square error of fitting.    -   7. Measuring the impedance of the human body between sensing        electrodes by removing effects of stray capacitances of the        measured segment of the human body and current losses outside of        the measured segment of the human body.    -   8. Calculating the parameters of the Cole model including        resistance at an extrapolated infinite frequency, resistance at        an estimated zero frequency, characteristic time of relaxation,        alpha exponential symbol of relaxation time dispersion, goodness        of fit parameters, and giving the result of the sum of least        square error of fitting.    -   9. Performing statistical tests for goodness of fit of the Cole        model. In the case of large modelling error by the Cole model,        various improved models of the human impedance will be tested        for modelling error until the modelling error decreases to a        satisfactory level.    -   10. Measuring daily changes of extracellular and intracellular        water mass with the individualized model holding to and updating        a quasi-stable extracellular to intracellular water mass ratio.    -   11. Measuring changes of lean body mass, fat mass, and protein        mass with the individualized model of the human impedance. The        individualized model of the human impedance is fitted to the        measured impedance data at preset frequencies while using five        constraints which are the ratio of lean body mass to total body        water; the fixed ratio of lean cell mass to intracellular water;        the fixed ratio of protein mass to lean cell mass; the fixed        ratio of total body mass to bone mass; and the fixed ratio of        extracellular protein mass minus fraction of bone mass to        extracellular mass.    -   12. Providing options and taking advantage of serial        measurements in the same subject. It can use a priori        information regarding predictable changes of body composition        which can be obtained from the method for the analysis of the        change of body composition and hydration status and for dynamic        indirect individualized measurements of the human energy        metabolism in U.S. patent application Ser. No. 14/541,033.        Herewith advantage is taken from the knowledge of likely trends        of changes of the body composition to improve validity,        consistency, reliability, stability, and robustness for improved        predictions of results. The standard deviation and confidence        interval measures of results are calculated and optionally, a        trend prediction of the results is given.    -   13. Using the apparatus to provide measurement results to the        method: the measured extracellular water mass on day k ECW_(k)′        can be used in Eq. 148 and Eq. 150; the intracellular water mass        on day k ICW_(k)′ can be used in Eq. 149 and Eq. 150; the        resistance of the human body at an estimated zero frequency with        constraints to assess body composition R₀ ^(BC)′ can be used in        Eq. 144 and Eq. 148; the resistance of the human body at an        extrapolated infinite frequency with constraints to assess body        composition R_(∞) ^(BC)′ can be used in Eq. 145 and Eq. 149; the        resistance of the human body at an estimated zero frequency with        constraints to assess hydration status R₀ ^(HS)′ can be used in        Eq. 159; the resistance of the human body at an extrapolated        infinite frequency with constraints to assess hydration status        R_(∞) ^(HS)′ can be used in Eq. 160; the lean body mass on day k        L_(k)′ can be used in Eq. 150 and Eq. 248; the fat mass on day k        F_(k)′ can be used in Eq. 151 and Eq. 249; the protein mass on        day k P_(k)′ can be used in Eq. 250; the lean body mass change        from day k−1 up to day k ΔL_(k) can be used in Eq. 116, Eq. 118,        Eq. 152, Eq. 201, Eq. 207, and Eq. 218; the fat body mass        change, ΔF_(k), from day k−1 up to day k can be used in Eq. 116,        Eq. 118, Eq. 153, Eq. 202, Eq. 208, and Eq. 219; the lean body        mass change, ΔP_(k), from day k−1 up to day k can be used in Eq.        116, Eq. 235, and Eq. 259.    -   14. Using the apparatus to accept results from the method from        the parent U.S. patent application Ser. No. 14/541,033: the        previous changes of the glycogen store change ΔG_(k) can be        obtained by Eq. 111, replacing the less accurate calculation of        Eq. 359. The previous changes of the protein store change ΔP_(k)        can be obtained by Eq. 113, replacing the less accurate        calculation of Eq. 358.

As referred to herein, the term “computing device” should be broadlyconstrued. It can include any type of device including hardware,software, firmware, the like, and combinations thereof. A computingdevice may include one or more processors and memory or other suitablenon-transitory, computer readable storage medium having computerreadable program code for implementing methods in accordance withembodiments of the present disclosure. In an example, a computing devicemay be any type of conventional computer, such as a laptop computer or atablet computer or a desktop computer. In another example, the computingdevice may be a type of network device such as a router or a switch. Inanother example, the computing device may be a smart television or ahigh definition television. In another example, the computing device maybe a battery powered Internet of Things (IoT) device. In anotherexample, a computing device may be a mobile computing device such as,for example, but not limited to, a smart phone, a cell phone, a pager, apersonal digital assistant (PDA), a mobile computer with a smart phoneclient, or the like. A typical mobile computing device is a wirelessdata access-enabled device (e.g., an iPHONE® smart phone, a BLACKBERRY®smart phone, a NEXUS ONE™ smart phone, an iPAD® device, or the like)that is capable of sending and receiving data in a wireless manner usingprotocols like the Internet Protocol, or IP, and the wirelessapplication protocol, or WAP. This allows users to access informationvia wireless devices, such as smart phones, mobile phones, pagers,two-way radios, communicators, and the like. Wireless data access issupported by many wireless networks, including, but not limited to,CDPD, CDMA, GSM, PDC, PHS, TDMA, FLEX, ReFLEX, iDEN, TETRA, DECT,DataTAC, Mobitex, EDGE and other 2G, 3G, 4G and LTE technologies, and itoperates with many handheld device operating systems, such as PalmOS,EPOC, Windows CE, FLEXOS, OS/9, JavaOS, iOS and Android. Typically,these devices use graphical displays and can access the Internet (orother communications network) on so-called mini- or micro-browsers,which are web browsers with small file sizes that can accommodate thereduced memory constraints of wireless networks. In a representativeembodiment, the mobile device is a cellular telephone or smart phonethat operates over GPRS (General Packet Radio Services), which is a datatechnology for GSM networks. In addition to voice communication, a givenmobile device can communicate with another such device via manydifferent types of message transfer techniques, including SMS (shortmessage service), enhanced SMS (EMS), multi-media message (MMS), emailWAP, paging, or other known or later-developed wireless data formats.Although many of the examples provided herein are implemented on serversin a datacenter, the examples may similarly be implemented on anysuitable computing device or computing devices.

The present subject matter may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent subject matter.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present subject matter may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Java, Smalltalk, C++ or the like,and conventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present subject matter.

Aspects of the present subject matter are described herein withreference to flowchart illustrations and/or block diagrams of methods,apparatus (systems), and computer program products according toembodiments of the subject matter. It will be understood that each blockof the flowchart illustrations and/or block diagrams, and combinationsof blocks in the flowchart illustrations and/or block diagrams, can beimplemented by computer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general-purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present subject matter. In this regard, each block inthe flowchart or block diagrams may represent a module, segment, orportion of instructions, which comprises one or more executableinstructions for implementing the specified logical function(s). In somealternative implementations, the functions noted in the block may occurout of the order noted in the figures. For example, two blocks shown insuccession may, in fact, be executed substantially concurrently, or theblocks may sometimes be executed in the reverse order, depending uponthe functionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel methods, devices, and systemsdescribed herein may be embodied in a variety of other forms.Furthermore, various omissions, substitutions, and changes in the formof the methods, devices, and systems described herein may be madewithout departing from the spirit of the inventions. The accompanyingclaims and their equivalents are intended to cover such forms ormodifications as would fall within the scope and spirit of theinventions.

What is claimed:
 1. A method comprising: at a computing device todetermine a set of indirect dynamic human metabolism parameters: using asensor on an individual to acquire a set of electrical measurements;combining a ratio technique with a canonical model form technique;performing a series of mathematical calculations on the acquired set ofelectrical measurements to determine the set of indirect dynamic humanmetabolism parameters for the individual based on the combined ratiotechnique and the canonical model form technique; and in response toperforming the series of mathematical calculations on the acquired setof electrical measurements to determine the set of indirect dynamichuman metabolism parameters for the individual, generating a trendregarding the set of indirect dynamic human metabolism parameters. 2.The method of claim 1, wherein the ratio technique is the individual'sdaily ratio of a lean body mass change velocity to a fat mass changevelocity and is called an R-ratio.
 3. The method of claim 1, wherein thecanonical model form technique comprises of at least one of a CanonicalModel Form of Human Energy Metabolism and a Self-Adaptive Input OutputModel of Human Energy Metabolism.
 4. The method of claim 1, wherein theset of electrical parameters comprises: a first voltage source; a firstreference resistance; a first excitation electrode attached to a plantarsurface metatarsophalangeal area of at least one of the first foot andthe second foot wherein the foot is based on the generation step; animpedance segment of at least one of the first foot and the second footwherein the foot is based on the generation step; a second excitationelectrode at the highest elevation and medial portion of the plantararch; a second reference resistance; and a second voltage source.
 5. Themethod of claim 1, wherein the set of indirect dynamic human metabolismparameters comprises: a daily change of lean body mass; a daily changeof body fat mass; a daily change of protein mass; a daily utilizedcarbohydrate intake; a daily utilized fat intake; a daily utilizedprotein intake; a daily rate of carbohydrate oxidation; a daily rate offat oxidation; a daily rate of protein oxidation; a daily parameter forenergy flux from carbohydrate pool to fat pool; a daily parameter foruncounted energy; a daily energy density of the lean body mass change; adaily energy density of the fat mass change; a daily ratio of lean bodymass change velocity; and a daily ratio of fat mass change velocity. 6.A method comprising: generating, at a first excitation circuit, a set ofelectrical parameters for a first foot of a human body; generating, at asecond excitation circuit, the set of electrical parameters for a secondfoot of the human body; sensing a voltage measurement of the first footand the second foot; collecting, via an input channel of a controllerunit, the voltage measurement and the set of electrical parameters forthe first foot and the second foot to create a digitized voltage signal;controlling a measuring sequence of the human body, via an outputchannel of the controller unit, by utilization of the digitized voltagesignal; processing the measure sequence, via a processor unit, to obtaina plurality of metabolic parameters for the human body; performing aseries of mathematical calculations based on the measure sequence andthe plurality of metabolic parameters for the human body to determinemeasurement errors; and in response to determining the measurementerrors, calculating a resistance of the human body at an estimated zerofrequency and an extrapolated infinite frequency.
 7. The method of claim6, wherein the set of electrical parameters comprises: a first voltagesource; a first reference resistance; a first excitation electrodeattached to a plantar surface metatarsophalangeal area of at least oneof the first foot and the second foot wherein the foot is based on thegeneration step; an impedance segment of at least one of the first footand the second foot wherein the foot is based on the generation step; asecond excitation electrode at the highest elevation and medial portionof the plantar arch; a second reference resistance; and a second voltagesource.
 8. The method of claim 6, wherein the sensing comprises: a firstvoltage sensing electrode attached to a plantar surface of the firstfoot anterior heel area and to a voltage measuring device; and a secondvoltage sensing electrode attached to the plantar surface of the secondfoot anterior heel area and to the voltage measuring device.
 9. Themethod of claim 6, wherein the controller unit is a microcontroller unitwith the output channel and at least 10 input channels.
 10. The methodof claim 6, wherein controlling the measuring sequence of the human bodycomprises: a part one stage one measurement wherein an excitationcurrent flows through a stray capacitance outside a measured segment ofthe human body; a part one stage two measurement wherein the excitationcurrent flows through the stray capacitance outside the measured segmentof the human body and through another stray capacitance of the measuredsegment of the human body; and a part one stage three measurementwherein the excitation current flows through the stray capacitanceoutside the measured segment of the human body, through the other straycapacitance of the measured segment of the human body, and through themeasured segment of the human body.
 11. The method of claim 6, whereinthe processor unit is a digital processor unit.
 12. The method of claim6, wherein processing the measure sequence comprises: running a sinewave fit algorithm to determine an offset, an amplitude, and a phase ofthe digitized voltage signal; processing a part one stage onemeasurement to determine an admittance of a plurality of excitationelectrodes, an admittance of a plurality of sensing electrodes, anadmittance of segment impedances interspaced between the plurality ofexcitation electrodes and the plurality of sensing electrodes, and anadmittance of current losses through the first foot and the second foot;processing a part one stage two measurement to determine a straycapacitance of a measured segment of the human body; processing a partone stage three measurement to determine complex impedances at multiplefrequencies of the measured segment of the human body; processing a parttwo stage one measurement to perform a Cole model curve fitting to thecomplex impedances at multiple frequencies of the measured segment ofthe human body; processing a part two stage two measurement to perform astatistical test goodness fit of a chosen model for the compleximpedances at multiple frequencies of the measured segment of the humanbody in order to obtain a best fit model; processing a part three stageone measurement to determine a quasi-stable ratio of an extracellularwater mass to a total body water mass; processing a part three stage twomeasurement to determine the extracellular water mass and anintracellular water mass; and processing a part three stage threemeasurement to determine a lean body mass, a fat mass, and a proteinmass.
 13. The method of claim 6, wherein the plurality of metabolicparameters for the human body comprises: an extracellular water mass; atotal body water mass; a lean body mass; a fat mass; and a protein mass.14. The method of claim 6, wherein performing the series of mathematicalcalculations based on the measure sequence and the plurality ofmetabolic parameters for the human body to determine measurement errorscomprises: calculating an error estimation of a lean body mass, a fatmass, and a protein mass change; obtaining a glycogen store and aprotein mass measurement from a prior day; computing the glycogen storechange and the protein mass change from the prior day through the use ofa state space mathematical model and a ratio technique with a canonicalmodel form technique.
 15. A system comprising: a first excitationcircuit for a first foot and a second excitation circuit for a secondfoot; a first voltage sensing electrode for the first foot and a secondvoltage sensing electrode for the second foot; a controller unit to:collect, via an input channel of a controller unit, the voltagemeasurement and the set of electrical parameters for the first foot andthe second foot to create a digitized voltage signal; and control ameasuring sequence of the human body, via an output channel of thecontroller unit, by utilization of the digitized voltage signal; and aprocessor unit to: process the measure sequence to obtain a plurality ofmetabolic parameters for the human body; perform a series ofmathematical calculations based on the measure sequence and theplurality of metabolic parameters for the human body to determinemeasurement errors; and in response to determining the measurementerrors, calculating a resistance of the human body at an estimated zerofrequency and an extrapolated infinite frequency; and a housing unit.16. The system of claim 15, wherein the controller unit is amicrocontroller unit with an output channel and at least ten inputchannels
 17. The system of claim 15, wherein the processor unit is adigital processor unit.
 18. The system of claim 15, wherein the housingunit is a standup scale to contain the first and second excitationcircuit, the first and second sensing electrode, the controller unit,and the processor unit.
 19. The system of claim 15, wherein the measuresequence of the human body comprises: a part one stage one measurementwherein an excitation current flows through a stray capacitance outsidea measured segment of the human body; a part one stage two measurementwherein the excitation current flows through the stray capacitanceoutside the measured segment of the human body and through another straycapacitance of the measured segment of the human body; and a part onestage three measurement wherein the excitation current flows through thestray capacitance outside the measured segment of the human body,through the other stray capacitance of the measured segment of the humanbody, and through the measured segment of the human body.
 20. The systemof claim 15, wherein the plurality of metabolic parameters for the humanbody comprises: an extracellular water mass; a total body water mass; alean body mass; a fat mass; and a protein mass.
 21. The system of claim15, wherein the processor unit, to process the measure sequence toobtain a plurality of metabolic parameters for the human body, comprisesimplementing: a sine wave fit algorithm to determine an offset, anamplitude, and a phase of the digitized voltage signal; a part one stageone measurement to determine an admittance of a plurality of excitationelectrodes, an admittance of a plurality of sensing electrodes, anadmittance of segment impedances interspaced between the plurality ofexcitation electrodes and the plurality of sensing electrodes, and anadmittance of current losses through the first foot and the second foot;a part one stage two measurement to determine a stray capacitance of ameasured segment of the human body; a part one stage three measurementto determine complex impedances at multiple frequencies of the measuredsegment of the human body; a part two stage one measurement to perform aCole model curve fitting to the complex impedances at multiplefrequencies of the measured segment of the human body; a part two stagetwo measurement to perform a statistical test goodness fit of a chosenmodel for the complex impedances at multiple frequencies of the measuredsegment of the human body in order to obtain a best fit model; a partthree stage one measurement to determine a quasi-stable ratio of anextracellular water mass to a total body water mass; a part three stagetwo measurement to determine the extracellular water mass and anintracellular water mass; and a part three stage three measurement todetermine a lean body mass, a fat mass, and a protein mass.